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IXOXO.MIC CYCl.KS: THKIR LAW 
AND CAU.^E 



CIIAPTKii I 



INTRODUCTION 



rilKHl-; is a considcralilc iiiianiinity of opiiiiou ainoiiK 
experts that, from the purely ecimdinic point of view, 
the most ^feueral and characteristic plienomeiion of a 
chaiiKiiiK society is the el)l) and flow of economic Ufe, 
the alternation of energetic, buoyant activity with a 
si)iritless, depressed and uncertain drifting- During the 
creative period of the rhvthmic change each factor in 
production receives an augmenting income, and the 
nnitual adjustment of interests in the productive 
process is hroughl about in a natural way. primarily 
through the operation of comii(>titive law. The jieriod 
of decline in the cycle presents a sharply contrasted 
a>pect of industry. With the organization of capital 
and lal)orat first unchanged, tlu^ amount of the product 
tails; each of the interoted factors seeks at l(>ast to 
retaui its absolute share of t!i(^ product; friction and 
strif(> ensue with a threa1(Mung of the di>ruiition of 
industry. What is the cause of this alternation of 
periods of activity and depression'.' What is its law? 
1 hese ar(> the fundamental problems of economic 
dynamics the solution of which is otTered in this Essay. 
Political I']conomy began to make progress in a 
rational way wlicii ihr riiysiocrats ]m\ fortli their 
doctrine of the dependence of all forms of economic life 



lu'iiiiii/iiic ('j/iii.s: Till If Ltiir mill ('ausc 



upnii ,i;ri-iciilinr('. Aniitlirr im(iiii('IiIihi> ^icp was taken 
in the (lircclinii nl' tlicdi'rtical (Icvcliipnii'iit wlicii tlic 
Mnjilisli ('(■(inMiMi--ts I'liniiuiatcd llic law nl' (liiiiiiii-liiiLti 
rctunis ill au,riculturc ami traced it> all-|)ei'\asi\e 
iiilliieiicc in the j)roiiiiei iun and di^t rilmtion (if the 
product n|' indu-tr\-. The de-idefatiini nf economic 
dynamics at tlii' ])resent time is the disco\-ei-y of a hiw 
that >hall l>e to a chanjiinij; Miciety what the law of 
diniini>hinu: return^ in agriculture is to a Miciet\' in a, 
comparat i\('ly static condition. 

The full truth in the old I'hy.-iocratic doctrin.' has 
not lieen exploited. The Department of Ajiriculture 
of tlie I'niied States I'ealliiins the central idea of the 
doctrine in ii- motto: " Ajiricultuic is lh(> I'oundatioii 
of .Mamit'acture and ('onunerce," and in the spirit of 
thi- motto i; pulili-hes in\-alualile statistical data. 

It is pro\'erliial that the t'armer i> at the mei'cy of the 
weather. If it he true that the explanat ion of economic 
cycles i< to lie found in the law of -uijjily of a^iricultural 
product-, it is >urely wi-e in a study of rhythmic eco- 
nomic changes to iiKjuire uhcthei' the law of the clian^'- 
inii -upply of I'aw mateiial i> not a>sociated with a law of 
chan^:inti- weather. N then* a well-defined law of cluuij^- 
injr weather'.' 

Supposini;- that it i- i)os>il)le lo disco\-er that the 
weather p;i>se- thi'ou^h cycles of delinite periods and 
detiniti amplitudes, it will then lie necosai'y to .-how 
how the cvnp< are affected liy the wealhei' and how the 
cycles of the we;)th(M' are rcjjroduced in cycles of th(> 
yield of the principal cnjps. 



I ulriiili/chdii 



I 
1 

1 



^^'!H■Ii the clKiiitics in tlic physical yield nf the crops 
arc sliiiwii 111 lie (lc|ieiiileiil ujx)!! chan^ic- in the weath(M", 
the next ^laue in the in\(--tit;at inn is to cdimect tlio 
yield will, its \-;dnc. and this iii'iny:s one face tn face 
with aniither un-<il\-ed pi-nhlein in thcdrclical ecdnnmics. 
The nh .-t I'ccent phase i>i ecuMunic thediy njiens with a 
(iesriiiitiun (if tiic "law nf demand," which fnun the 
time nf ( 'ouiMdt , 1 )upuit , and ( ids>en has been assiinie(l 
in all theoretical dis(aissidns, hut thefe ha> been no 
method for findii'.fi the statistical equation to the law. 
It will lie neccssaiy to o\-ercome the ditiicidties of this 
pi-dhlem liefdi'e a snlutidti can he dl'fei'cil df the more 
fundamental inc|uii-y as to the law and cause of cycles in 
economic phenomena. 

Wlcn the physical yield of the cfops has. on the one 
hand, heeii ivl.ated to the cycles of the W(>ather and, on 
the other, to the jirices of the respecti\e cfops, it will 
then he possible to take the final stej) and to show how 
the cycles in the physical yield of the crops produce the 
cycles in the acti\ v of industry and the cycles of 
general prices, and how, finally, the law of the cychvs of 
the crojjs is the law of I'lconomi'' ( 'ycles. 



('ii\rri;i{ ii 

< '^■(■|.l:s ol' KAINIAI.I. 

"The lii-.sl iliiim that in my oiiinjini ouiilii \n \iv ddur Inwards 
inakiiiK tlir (il)scrvatiniis useful f(Ji- sciciililii' pur|ii.M s i> in p( rfMriii 
llial kind .if iiK.ir prrlVrt a\cia-ilit; uhich is alToldrd l,y the har- 
liiniiic aiialy-H. 'I'liriv is a critaiii aUKJUnt of avcrauiiit; dotic, \nit 
lliat i> diii lly daily aMiaiT's, uilli najtithly avcrasiis. and viarly 
avrraurs: liul tlir hhhv |iiifri-t aviTa^iiii; i.f I lie liariiiniiic analysis 
Would LMM' I lie lc\il nf III,, variation of the plirnoinrnon." 

■ I.uiii) Ki:i.\l\, //, ///x tistiniDiii/ In/on tin MdioioliKjiail Con,- 
mitta <ij III, UKijnl Suriftij. tS7>:. 

!• lio.M the pdiiit nf view of tlic rcl;iti(Hi of chaiifriiif;- 
weather to the \afyiim fruit fiihie-- (d' a-ific'ilttu'e. the 
most important taelor- that are usually iiichided in 
the term, ucatlier, are temperature ami ra^ fall. \\v 
l)i%n,i ,,iir iinc^tiiratioii with this common ludud' and 
in((U!re. in thi- chapter, whether the varyinji amoimt 
ot animal rainfall is -iiliject to any simple law. 

In order to carry forward the iiKjuiry as to the exist- 
ence (d' ;i law of ammal raiidall an analysis must he 
niade <d' a lono- record of i>reci|)itation. Our choice of 
a record is liimted l.y two conditions: l'"irst. our object 
ni invest iuatinu: the periodicity (d' raiidall is the hope 
of Ihrowinjr ijain upon i he periodicity in the yield of 
the crops, and this expectation oliviously maJ<es it 
desirahle that the record of raiidall shall he as repre- 
seiitati\-e as po-^ihlc ,d' the conditimi;, of precipitation 

4 



Ci/'ics (if h'liiiifall o 

ill 111' Iciuliiiii crnp nrra: ^crondly, as tho existing 
iiiclcnroln^iciil rccdnls ai'c of iinciiual Iciit^ths and of 
vaniui!; rcliahiiity. it is nccc--:irv to tat<i' tlic hcst ionj? 
rcfords tiiat cau he found wiliiiii tiic limits of tlic ci-oj) 
ai-ca. 

'riic principal fciiion of y;rain pi-oduction in the T'nitcd 
State- is in the .Mississip|)i X'allcy, ImiI the inctcoro- 
lotjical records of the .Middle West do not exti'iid throuf^li 
a loiifr period of time. In order to achieve the two ends 
"t Iiavin^ a lon^ i-ecord of i)recipitati(in and of having 
the record typical of the condition- in the grain area, 
the de\ice has heen adoi)ted of in\ est igating rainfall in 
the Ohio \alley uhicli affords the longest record oh- 
tainalile in the neighborhood (if the central Mississip{)i 
region and of showing that the rainfall of our lead- 
ing grain >tate, Illinois, follows the same law as the 
rainfall of the Ohio \';dley. 

The stations in the Ohio X'alley with long lainfall 
records are .Marietta, Portsmouth, and Cincimiati. 
Their mean antuial rainfall sinc(> \s:]\\ is gi\('n in 
Talile I ' of the .\i)pendi\ to this chapter. The graph 
of the course of rainfall in the Ohio N'alley since ISIV.) 
is traced with other grajihs on I'igures 4, ."), .and (>. The 
liroMem that must now l)e faced is the iiuestion as to 
whether the se(iuence of aiuui.al rainfall in the Ohio 
\alle\- toliows ;i simple law, .and if .-o, to give a (luaiiti- 
tative tormulation of the law. 



' 'I'lic ihila were t^ikcn frum linllitni W of the \Vc:!t|ii.r Bureau of 
the I'liilnl States ami ffdlii the .\niii,nl III iniils ui' the ( 'liicf (jf the 
W'latlicr liurrau. 



i.nitiiijiilc Cfiilis: Till I r l.dir (in,/ C-nisc 



/Ik I SI III I'durii r's Till iiii ni 
A pivliiiiiii.iry (AainiiiMlidii nf th,. i;iint;ill ,|,.,ta ,,f H,,. 

Ollio \nll,.v |,,„1. In tl„. ,.,,„rlu>i,„| (1,..|, ,1,,,,.,, 1^ ,„,,i,. 
.•ll)ly un M'cul;ir tlTlid t,. Ihr <|;il;i. tli.'il i> to say, then. 
i< prohaMy no t.^ndciicy of th,. fainlall t.. iiuTcax' .•oii- 
linuMU>ly or to (IcTca-c coiitiimou.lv with th,' flow of 
''""■■ " i-^ ""'• 'I'.-il when the amount r,f i-aiiilall is 
•■'"■'■'■''"'•'1 \^ill' 'iiMc. thr .•ocinciciit ni coiTrlatiou is 
^= - ---7 ±. (»:.'). wliciv thd'ocHicicnt is three lir les its 
I"-"'"'''!'' <■'■'■'.!■ and i> Ih.'icloi.. sufTfrrstivc of a (Iccivasc 
'" ""' ;i'noiiril of raiiilall will, the (l.,\\ of time. Moiv- 
<'\"f. if a straiiiht line i^ titted totliedata, t he indical.'d 
="i"";'> 'l<'<Tease in the rainfall is seven hundivdths of 
•'" i'"'''- '''111 these laets air no justifieation for hold- 
'"- '" =' ^•■'•ular decrease in the amount of antnial 
'•''"''='ll- •■'-"■. i" <1h> fii'st place, if lh(«re are .-yeles in 
the ain(.iint of the rainfall, the low ,1 ,ce of the ,.!,- 
served correlanon mifrht I.e due to th.' data of rainfall 
includit.^ inc(,mplete cvch-: it, ;!„. see.,nd phur. the 
record is drawn from oidy three stations and heeaiise 
of the limited iiuml)(>r of stations mifiht j-ive an acciden- 
tal, low d(-frree of correlation hetween amount ..f rain- 
fall and tune; and in the third place, improvements 
in the method of takinjr the ol.servr.tions niifiht have 
introduced chaiiKes that would account for the ob- 
served small aiumal d.'crease in the amount of rain- 
fall. In view of these eonsiderations. it is probably 
b.st to imneed with our [,roblein or, the as.sumption 
that there is no secular trend in the amount of annual 



( 'ijili s 1,1 lunnfiill 



i;iiiil;ill. It ilii- ;i---uiiipti(iii !< true it tnllnw- that, in 
.-ill prdlialiilil y. the cnur-r < it rainfall in I lii' ( 'liin \allcy, 
i> cM-liral. Ill' a ciiniliinat inn (it ryclc^. 

In an iniliicli\c i iwalnirnl <il any tdrni ni' rhviiiniic 
i>y cyclical chanj^c it i> iiccc-~ai->' thai the inctlmd 
adnpicd ~liall -ati-t'\ Iwu cuiiilil iuii- : |. It -hall he 
ci iii-i-lcnt with iccii^ini/cil mat hcmal ica! jifncoscs; 
■_' : It -hall altniil mean- nt tc-iini;' llic dciiicc uf prnlia- 
liility that the fc-ults afc nut chance |ihcn(iincna. 
I nlc-- the inellind |-e-t-- deafly ii|)iin an aji|ifii\ed 
mat lieiiial ical [H'lice--. it i- -cai'ccly |)(i--ilile id -a\' 
whet hef I h ■ at taiiied fc-iill- nia> In it lie en I i rely Inrnial ; 
and iinle-- the lindin^- are tc-ted tnr the dciiree nt' their 
pfMliahility, there i- nu a--iirance that the adduced 
c\clc nia\' imt he a chance nciairieiice. The literature 
in which rh\lhiiiic pheiKMiieiia are treated in a -tati>- 
lical way teem- with tallacie- and uncertaiiil ie- that 
illu-tlate the need nt nli-ervitlji' the alinVC I'l mdit i(ili- ; 
tnr the Inethnd t're((UenI l\ ailn|ited nt -mnntliincr tli(. 
data i- -n arliitrai'N' that niie i- at a In-- tn kimw \\ heiher. 
after all, the alleiicd lierind icit >' nia>' imt . in tact . he due 
tn the pi'nce-- i>\ -innntllillU. alld, ill additinll. nlie i- 
let! in ilnuht a> tn whether all iliclelinite numher nf 
c>'cle- nt her than the |iarti(ailar niie addui'cd ini^ht imt . 
with equal nr <ireater prnhahility, he nhtaincd frniii tlic 
>;ime d;ita. 

The iiietlind that was einplnyed tn re;icli the re-u!ts 
nf this clia|)ter rots upon the analy-i- iincnted hy 
.In-eph I'niirier,' whi!'h is called, in Ijiiili-h trc.alises, 

I lie lllli.-t plaiii.^lijiliU' r\| ci-il lull i,|' liilirirl'- tliciircll; I- jn 



8 



/•'ciiniiiiiir Ci/i-lis: Till ir I, mi' ninl ( 'uuse 




FiiaiiK 1. 



lirirtriMriic .■iii;ilysis. Tlic piiirct mn ,,f ih,. tuctliod 
uhcrrliy till' linditi!^-. in.-iy l.c -i||,|,.ciri| i.. the lot (if 
pfMli;il,iliiy is ihc wiiik (if I'r,if(-^,.r Anliiir Sclm^irr ' 
(>t .M;iiich('-tci'. 

\\ f Ili.iy liciiili (lie prc-clil;iti(ill (.f the tiiclli,,i| \\ it), ;, 
(Icliiiiliiiii (if ;i -, TIC- n\ terms tli;it coii-tjiiitly iccur in 

Ilic trcaliiiciil (if [icriddic |)|:r- 
tKinicMa. I'iiiuic | \\i|| facili- 
l.itc the fApii-iiKin liy ;itT(ir(liiiti; 
n jiivipliic (Ic-i ri|)ti(iii (if the 
l('rni> <lc;ill w iih. 

>npp(i-(' tlial the piiiiit (} 
iiKiM's iiiiit'dfiiily ill til,, cii-cli. 
<|f I'l^iirc 1 . that is Id -;iy, Mip- 
pii-c thai the |ii,i,it (J (ic-crilics 
'■<|ii;il ;ii'-^ ill <'i|iial tiiiic-, and, llicrcfdrc, pnipurt Knial 
an- m diflmiii tinM.-.. r|„,,,_ |f ,i„. ,M..a-i;rcnicnls ,,f 
''"' •"■'■■' "'•' 'I"' •■i''-l(- arc made frdiii i1h> pdim .| ..,,,,1 

the IVrkdMii^ ,.\- t||n(> i-, lictriin \^||,,,, (J i^ _.|, /. ,j„, 

.•niLi'c .1 <) /•; 1. called the nntilc ai cpuch, (ir simply 

leiinci-.sdui, w,,iL: VV. .-, ,.w/,„„,7/„,.,„ ,/, l„rh,il,„r. Ii, Pi.rman'.s 
linirlisli tniiisliiiK.ii li.e in aliiicut is fdiiiul (ni pp. l;;7 _>]_'. 
' 'I'lic fiiii(l:iiiiciil.il iiiciiKiir, (if IVofosdi- SclMi>l(r .miv 
• n„ tl„. hivcsii-itidii ,,|- lli,|,l,n |',.,i,„licitics uiil, Appjicatidn 
td a Suiiposcl 2.; Day I".mo,| ,,1 M. i, ,,n,l„g„,,| V\,vu,nnru:,.- 
Td-n.-'Iriiil MifiiHitisni for Maicli, IMIS. 

'•The I'cridddHTam (,f Ma^iiclic Diciiiiaiioi, a> dliiaiii, ,| Inmi the 
n'Cdrdsdf tlicCivcnuirh Olis, nateiv dining; ihe \,ar~ |s71 is'.i.-,." 
Cainhriihir l'liiliis„i,l,i,id Sornti/ Tiiuisarlnni.-, \d|. Is. \sw. 

•On the Periddicltydf Suiispots." I>l,ili,.<i,pliic„l Transudions of 
tlic /t'lii/iil Siiri(li/iif l.im'liiii, A. \ i.L .'(ii;, jdiiti. 

-Tho Periddoiiran, aid ii.- (tpmal Anai.-y,- J'ri,ru,!i,iij.< ,.f 
the Ifoynl Stx-idi/ tif J.oiiiliin, A. \ul. 77 pioii. 



Ci/rtt's (if luiiiifiill 







the i|inrli (if llic iiiiitMfm rirciilar imitioii. Tin- 
t;iiliu~ III' llic ciiili' 1-^ tlic aitiiilil ii(|i- lit' till' iiintiiiii; 
ihr liinr nl Hniliy; (ilirr aluUllil tiir ril'clr 1-- (lir 
|irtliill lit' tlir llliitiiili; lllf nilHi lit' .t (.> Ill till' 
rllrUlntrrrlirr nt lllC (ll'clc 1> the |lli;i-(' lit llir Illn- 

I mil. 

1 1' frmii each pn^ii khi nt () a pi riirnilinilar is dinpiicd 
U|i"ii |1m> (liaimlrr nt lllr cilrlr, (! II. the font (if the 
liri|irnilirulai' will (li-i liiii' ;i >iiiiplr lianiiiiiiif iiiiilinn. 
I'hi' aiii|ililuii<' III till' ^iiiipli' liariiiiiiiic iiiutinii is (ni - 
liall III llir lariy;!' lit' llir iimt imi, that i<, imr-liait' tit' 0' //, 
III' the radius of the circlr. 'lln' priinii of the smipic 
hariiiii lie iiinliiiii is the iiitcrxal lu'lwri-u the l)a~-iii^5 
of 111.- point y* twirr tliioiiiili the >aiiu' position in tin' 
sanii' (lirri'tion. 'riic di-taiu'c of llir iioint /' from the 
miililli' of its I'aimc, (K is ;i ^inl|ll(' liarinoiiii' fuiii-tioii 
of till- t imc, O /' // a sin I «M < . '\ lu'rc n is the radius 
of till' ciirlc or till iniplitudo of the .-■inipli' harmonic 
mill imi '■ is tli(^ aniik; of epoch, and // is the an^lc dc- 
scrilicd liy the niii\iiiif point (^ in the unit of time. 'The 
period of the simple hai'iiionic inolinn is, in the aiiox'e 

'Jt . Ill ■ i 

( a-e. . Its plia>e is 

// Jtt 

liy:iire 1 presents a f^rapli of simple liarnionic mo- 
tion. As in Fi<>ure i, the point Q niii\e< uniformly in 
the I iiile; the point I' performs simple harmonic motion 
accoidinii to the formula (l -n sin [l>t^~^•\, where n is 
the amplituih' of the motion, or radius of the circle, c 
is the arit:le of the epoch, namely, .1 O E. and n is the 
arc ile>ciilied liy (} in the unit of time, if time is nieas- 



I(» I'.iiniintiir Ci/rhs: Thtir l.nir und din.sr 

lirril llpiin llir lllir li r. till- siiiii,,!!-; cinAc (,i' I'iL;iin> 2 
is llic niaph 111 Ihr liHii I lull, ,/ „ ,1,1 ,1/ , , ,, 



o «-- — il_ H i £ \ J < J A 

„ — ' — I 



I'll. I UK 2. 

'Nh' nil|iMrl;il|c.. «,(' Miiiplr l!;iriiiMtili- Iuiii-||M||> III 
the Stilily ()| priidilic plicniillictlll JildW, (Mil u\ llic |';ic| 

ili;it ;iri\' |)ctiMi|ic ciuac Imwrvcr cdnipli'X ' r.-ni \>r i\- 
liroM'il in.illM'in;ilic;iily liy ;i >crics dl' Minpli' li;iriiiniiic 
rilticlinn--. My the help of 1 uiiricr's ;in;il\H> ;i pen, idle 

I'uiiciioti may lir put m tlir Innn 

Oy '\o f "1 "'OS /./ T (I.J COS 2 l.i ■ II CO- .', U r . . . 

+ /). -in kt + b., sin _' l.f ■ /-;, -m ,{ kt -r . . . 
If in ( h, ui' jiiii . 

o, = J, sill (,; «, = .1,, sin c.; a,, = ,1 , sin f,; See. 
'», .1 1 c.- . I ; /), = A., cms ('.,; />., = /I, c.s <:,; A'C, 
\Vc tict, 

(2) !l = .!o • .1, Mil (A/ T r,) t- .1., -Ill (_' /7 • ,,,) 
+ .-Ji sin (:W.7 + e,) f . . . 

where 1/ i- exprc- ed as a scr:,> ,,f -inc-. In a -imilar 

'ii''iii"i''i'- c(|ualMiii ^ h may he cxpro-i'd as a >cri(..s of 

C(l,-illl'S, 

''I'lic frw exceptions to tlio t'cncral nile ;iii' (li-.ii-,.,l i,, the 
miitliciiuitical texts that (lfvcl<»i. I'l.iiiiii'.-, tlirmviii. 



5 



i 



('t/lirs of h'.inifall U 

(3) // = to t fl, (W (kl t ,) . n. (•<)« (2 /17 - e .) 

• n, CO-, (!{ /7 . ,) ♦ ... 

In llic ll-r <i|' I'lMliiii - ihcdiclii t'dl- till' |ilir|iii-r ot' 
:iM.il\ /.Ihli |icl|M(||c plr UniiM ii;i. \\f I'mIIhw ;i pi'MCCSS 
.•lll.lln^iPll^ 111 I lie ll-c III Tax 111 l'^ lIliiTclil ill I lie ^lllll ilcf 

i|riiiiiii-lt'.il mil- <il MiaMicinat leal (•(•niiuiiiii's. \\\ jar 
llic tiK-atci' pall f'l ( 'luirrint - puirici'i- liTatix' and (if 

>llli-ri|ll(lll \\iifl< (i| III-- -cliniil j- iia-cil llpdtl tlir as- 

-III, ijit lull tii.-it, it' till" (■(•uiiipiiiic iiiiirliiiii iiiMlcr iii\c-ti- 
Uali'iu i- // ./'i.r), tlii'ii /i.r f // ) may In- cxpainiril l>y 
'ra>liir-'- tliriuriii, and the tii-t tci'iii-- <il the xtic^ may 
!)(■ 11-1(1 a-< an appniMinal iun to tin' t'nrm ul' /'./•). Simi- 
larly, m (iiir u-i- (if l'"(iiiricr's -eric-, the alt cut ion will he 
fdcii— cd iipiiii a li\v hariniinics a- a lir-t ,i|)prii\imalliiii 
Im tiic -iiliiiiiin III' the prnlilcni in li.-ind dt' cxprcs.qi.K 
in niatlicnialical t'tnni llic pcriddicily nt annual rainfall. 
A--iimin^ lliat any pcriddic fiinclinn may he cx- 
pic.-x'd a-; a l'(!Uii('r scries, ihc proiih m is |)icscntcd of 
dclrrmiiiiiiK the \aiues nf the eoetlicieiil-. The series, 
as we kiKiu . is df the fdrm 

1/ f(t) - .lo f ((, cos l,t • II, .'(IS 2 l:t -1- . . . 
+ /), sin kt f /(., sill 2 /,/ f- . . . 

What are tlie \aliies of the lirst term and of the co- 
efiieicnts df the sines and cdsiiies' In order to dednco 
the necessary values, we shall lunc need of the foUow- 
iiij; Icmiiia : 

If HI and // are two une(iual intefiers and /. is i)ut ('(|ual 

•Jir , 

to ,., , then 



i 



12 Kc(),:n,nlr Cijcli.-i: Tlnir /.„-/• „//'/ Cause 

I II » iiil.i r,f< ,iU ,11 

/ ~iii iiiLt sill /,/,/ ill 0. 

/ -ill ////i/ ros /(/,-/ ,/t I), 

'I'll'' l('nini;i may in' j.rn\cil to l.c Hue l«y cv/iluatinfi the 
flinv iiitcKrals accnnlin-r to the UMial incthods. 'I'he 
fir-t intciifal, for i xaiiipliv licciHiirs 



rnl.t t'Ds /;/,■( dl \ 



But A- 



. ail,!, i nt ( 



' I ]cns{ni ii)kt + fos (,n * n)ht\(lt 

^ [sill (w n) Id sill (w . ii) Lty 
V -2 Un u]k ^ 2 (/// , n) /,■ J„ 

cciiuMitly, / ros mkt CDS nht <it --= 'J. 

With tlic aid of this Icuiina we may pi-o.vcl to cvalu- 
ato tlic cooflici.Mits in 1 ouri.rs srrics. If w,> intoKrate 
(lu> scries bet\ve(>n the limits o ami T, we get . 

l^ut all of the terms ("xcept th,- first oiv the right-hand 
side of the eiiuatioii will vanish, and coiiseiiuently 

//(Ml// 
j '/CO'/' .l.j ".//-.!„ 7', or.. U-/" y,_ 

Sinn. / /i/!,/7 is the ..-va of the original enrvo for one 

\vhol(. period 7', the constant t(-rm in Fourier's series is 
<'«iual to the value of the mean ordinate of the original 



curve. 



< '//(Yr.s ';/' h'dinfdll 



13 



'l"o (Ictoriiiiiio tlic value of (/|, multiply throughout 
by cos /,/ and integrate bctwcca limits a and T. 

a ' •• li 

/•T 

+ ^, I sin /,/ cos l.t <lt ^ . . . 
Or / f {t) t'lt^ l,t lit (If i i_'()sW,7 f//. >incc / i'n> l.t ilt and 

o ^> o 

I -ill It ens /,/ (// are both ('((ual to zci'o and all the other 

teiinson th(» ri(iht-han<l side of the eciualiuu, according 
to our lemma, disappeai'. P)Ut 



•^1 + cos 2/,/ 



// = H / • 



sin 2 I.I 
21.- 



T 



./■ 



/ ,0 !■' s l:t lit 



or *(, = J 



f\:.^U.It.j 2 

and as a result, we haxc 

"1 i - //('^ cn^ktdt. 

Therefon^ i/i is e()ual to twice the mean \alue of th(> 
product /i/)C(ts kt. 

in a similar mamior the value of any other coeflicient 
may he det(>rmin(Ml. Tak(\ for example, h Multiply 
throughout l)y sin nla and integrate between <i and 7', 



/ / (t) -in nit lit h„ I >M' nl:t ilt l,„ j ' ' ".'. ' 'It 



'T 1 cos 2 iikt 



"n 1 



sin2/(/,7r , T 



and, conse(iuentlv. />„ - 2./ "^ . lherof()re6„ 



14 hcdiiuttiii- Cijihs: Till if I.itir mill t'niisc 

'■^ '''i".''! '" twic.. ihc mean \alu( n| th,' pnidiict 
/(/) sin >il:l. 

IlaNiiii: fninid il,c a|ovl,raic \alii,>> ,,|' th,. .■,,.. Hi, a,. nl- 
'" I'Mn-icr'- xa-ic-. uv may n-av [.mrccl i,, (IrtiTmuic 
flHir-tatiMir;,l,.,|ui\;ilcnt-in ilii' ca-c nf annual I'aintall. 



'I III I'l nnilni/rn/n nf Ixnliifiill 

If the Icniitli ,,fa <'yrl,. .iraiiilall wnc knnw,, l„.tnn.- 

''■•""'■ 'I"' friMvlm- ,.x|.....iti,,n i,\ i'.Mn-i.a-'^ iln'.ircm 

U'Mil.i Millie- I,, ,l,.t,.rn'i; Imm th,. ,lala ni piviapita- 

ti'-n. Ih,. ampliiiiWr^ an.! pha^-. uf tl,,. harnmnir ,,,n- 

.-tiiiicni-. ,,f i|„. |',,iiri,a- -th- ,|<-cripti\ c ,,f th,> raintall 

•■>■'•''■■ ''"I' i" 'I'" pi-mI,],.,,, hriniv „. nf analyzjiu' the 

'■''"•■■•'ll'lata..lt|ir()|,i,,\all,.v,u.Mlnn,,t knnu ulu.th.T 

''"■'■'■ ■■"■(■ man\- vyAv^ ,„■ ,„i|y ,,n.. ryv\r ,„■, indeed. 

uliellier ihrre a IV ally eyelet at all. And there is nn 

slini-t inetlidd ,,f -nix inn th,, |,r,ilil,.ni. 

>upp(.-,v fur cxinnple, it were a-uine.l tn.m a prmrl 
'•"nMderati,.n. ih;;t M,,, aiiHuint ..f raintall i- affected 
I'.v Miiiv,„;t>, and. a- -iin-|»nt^ are known tn ,,eciir in 
P'Tiod. (,f alHMit el.-xen years, Mippn-e i, v|i,„il,l 1„. j„. 
''■'■'■'■'' •''•" '•"■ ""Miial rainfall will likewi^. ^hnw a per,,,,! 
"i vlrvrn y.'ais, jf ij,,. rainfall -lata ,,f th,. Ohi,, \all,>y 
•■n-e examined h.r .an ,'1,.\ ,.,, y,.ar- peri,),|, it will ]„■ jmind 
'•'■" '1"' 'l:ita yi,'l,| a ,1,'iiiiit,. amp!itii,le an,l a delmit,. 
''''•'^'' '"'• ••' <T''l'' "'■ ''l<'ven y.'ars, hiit this taet r^ „,. 
warrant tny h,)l,|iim t hal there i> a true rainfall peri,,,! ,,f 
• •iewii y,.ar~. iiv.'ry ,,ili,'r ^nuipiiiK "f th,. <ev,.nty-t w,, 
year- re..,,nl uill likewi..e show :i detinil,. amplitude 



( ' IJCU s (if Rill l: I nil 



1.") 



.'iml ,'i definite* plui^c. 'I'tic (|U('>ti(iii< tliat diic is in- 
IciTsicd Id lia\c ati~\v('i'c(l arc; .1 ' W'liat i> the law nf 
the 'i>tiiliut inn df I'lHirici' (•ii('fiici('iit< when tln' data 
arc analyzed tni' all pd-^-iiilc pcriiMU; and i 'J i h'i'v may 
llic tiMic cycles lie -epai'atcd 'V(,ni the accideiual, 
spiiriiiu- cyclc< that are nhtained when the dat;. ai'e 
c\liau>ti\ely analyzed'.' 

ill I'itiui'e .5 the re-iiIt- nt' a detailed, lalini'ior.s ex- 
aininalinn of the data nf annual rainfall in flu Ohio 
\'alley are pre-entcd in graphic t'orin. (In the axis of 
!il)scissa> are inca-Ufed, within a»i^ned limits, the 
])ossil)le leny:ths of cyclc< \i\ the 72 years of rainfall. 
Hy extendin;;' the calculations to 'M\ year-, we ohtain 
foi- ihe a-^-^umed periods a record of ])ossil)!e fecur- 
reiices \aryinji from 2, in case of the ])eriod of 'M\ 
year.-, to 24, in ca-e of the period of .'> years. On the 
axis of ofdinatcs afe measufcd the -nuares of the co- 
etiicients of the fii--t harmonic in the l''ouricr >eries 
coiTespondin<i to the leiifiths of ))efiods fecorded on 
the axis of aliscis-as. 'Ihe numerical \alues of these 
sepiarc- are >ii\'en in the fourth and eighth columns of 
'r.ahle II in the .\ppen(lix to liiis '■ha])ter. 'i"he method 
of dcri\inti the values may he illusti'ated !)y taking the 
cycie of S years, Sui>|)os(\ as a first approximation, 
that the e(iiiation to Fourier's series is j)ut in the alge- 
liraic form 

]l = F{t) = .lo 4- «i cos l;t t- />i sin Id = .l^ i .1, ■<in {H + c). 



Then tlie corresponding arithmetical values deriv(>d 
from the Ohio rainfall data are 



16 



Ecduoniic Ci/chs: Their /jiir <inil Cdnsc 




//ejuiej JO f^i/j>£/' ui jpn^.iJuJB Sl/j jo ajenbc 



( 'i/cli S llf UiliiiJuU 



17 



y = F{t) = 41.111 '.\.V.>, CO 



2t 2rr 

" / + 2.(i9 sin . I 






U.llt^ 4.1X -,i. r t +:U()° 41"). 

Tho Valiums (if the terms (i\. h\, A\ arc ropcctivoly 
(:M83!»)-, rJ.C.H.'^S.', (I.i:i25r-, and these \alues are 
Rivon in the ])n)|M>r columns of Table 11 in the Ap- 
IK'ndix. Ju Fitiure 'A, tho values of A' for the several 
periods are nieasure(l on the axis of ordinates. 

An cxaniination of l''isui(> '.i will illustrate the truth of 
a statement aiivauced a moment a^o. It is clear from 
the course of the p(>riodo}!;raj)h ' that if one were to 
take any ))eriod at random between the limits of 3 
years and 'M years, he would in every case obtain a 
finite value for tlie amplitude of the . elected cycle; and 
if, by chance, s(>lection should fall ui)on, say, IS, or 21, or 
2!l, or 'M years, an arfiument miKht be made with some 
degree of j)lausii)ility tliat u real cycle had been dis- 
covered. But, in truth, the real significance of no one 
cycle taken at random can t)e judged apart from its 
|)lace in the distribiitioi. of all the cycles that can be 
derived from the data. 

This last point is of fundamental importance. The 
only oi)ject of investigating eycles of rainfall or cycl(>s of 
economic phenomena is that th(> knowknlgc^ of the 

'Till' terms iicri()(i(ii;ra[)li ami iicricKldfirain were cniiicd ty I'm- 
fcssor Schustrr. 

Til'- |)('rio(ii)gra;iii i> the curve tr; "inn the \"aluc,s ef .1-: the 
peril II lijjjrain is the surface iietween the peridildjirajih ami the hase 
line t;iviiig the leiif:;ths of tlie |)erio(is. Schuster: "The IVriod- 
onmiu of Mugiioti.- Declination," \). WH. 



18 hciinninic Cijrl, s: Thtir 'jtii- innl Ciiiise 

'•"nstaul rcniiTriK'c nf the cy.-Io may place otic m a 
Iin,-iii,,n 1,, luiv-ccaiid iilili/c llic(lc|,ci„l,.,ii pluaniiMciia. 
'^'" ''"■ ''"'itn,! ,)f phciuinicna dcpciulcnt iipdii a cycle 
l-n-iipp,,.,.^ It, at r- cycle i> itself a real plieii(,iMen..n 
with a natural cause, and that c<,ii-;e,inent ly it peivj>is 
with ail ilicfea-c ill the tiutiii.ef of (liiserx at iotis. If, 



hii\\e\('f, ai 



1 appafctit cycle ,,f atiy leuiith taken at 



ratidnn, i.^ ..l.taiti.'d t'tvuii the uiwti data. ( wmild 

Mirely mi-peud his litne if he weiv \n ,-et aliniit the 
seai-ch tor itv cause, and were to derive conclu-idus hased 
lll'oii th.' hypnth.-i. nf th,. persi<|,.„,.,. ,,f the cause. 
'I'he cycio due to tornial. accidental causes must he 
discriminated from the cycles with natural causes. 

■|"h( M.par;itJon ,,f true cycii's from >p,u'ious or 
a.'cident.al cycles i> facilitated l,y the perio.joon.m ' of 
<>l)servatioii.. If. followitiM- i'roi.-M,r Sdnister. we call 
the s.iiiare .,( i he amplitude of any t;ivei. period the 
"intensity" of the i)eriod, then it may !,<■ said that the 
i"-"'':ilHhty of tliereality of a period is dej)eud..nt upon 
'!"• f^itio of its intensitx to the n,,,,,! intensity of the 
!"'nndoa;ram. Or, atiain lo||,,\vinn- I'n,f.'ssor Schuster. 
It we call the mean intensity of the [i.'riodofrram the 
'■-■XjH'.'tancy,- then the reality of a p.'rio.l is (iependent 
"l""i 'Ih' ratio of its intensity to the exp<.ctancy of the 
l"'nod,,ii,,nn. For instance, if in case of a -iven p<Ti..(l 
the ratio of intensity to expeci.ancy is. .say. 'A to 1, then 
i" "'"'I" onr case in twenty we should expect to ol.tain 
by chance a Kiv.ater amplitud,> than l|,e amplitu.je of 
tlH' pnrti.Milar period in .lue.tion. If. „„ the other li.Mid. 
' Scr till' iiiccciliiii; iiutc. 



Ci/ch s of h'liiiifiill 



19 






the ratiii were say, 7 n 1, a ^ircatci' fatio wduM imt 
(icciir l)y cliaiifc (incc in a tlinu>aii(l tiinrs.' 

Willi llii'-c t'ai-l- in iiiiiid. let u-^ ajiaiii cxainiiic \\\i- 
iirc .■>. It i- clear iliat the priiici|>al jicrioil^ needing 
altcnliiiii arc tlnoc I'opcct ivcly of S, L".», :\'A. :U\ ycai'<. 
Ii[ ca-c 111' the S ycai- cycle there can lie \cr.\ little 
(Idulit a:> til the e\i<tence (if a lr:ie ]iei-in(licity ap|)rnx- 
iinatiiiii; S years in lentith. 'I'he ratin of the M|uai'(' <if 
its aniplituile to the mean Mjuafe ainplitmle nl' th(> 
perindo^ram i> ti.71 tu 1. We may accurdiniily accept 
with cdiisideralile ennlidence the e\i>tence et a natural 
liei'iiid of i-ainfall m the Ohio \ alley approximating 
S year- in lenu;th. 

'The cycle of -VA years, inasmuch as the latio of the 
s(iuai-e of it~ amplitude to the mean s(|nare amplitude 
of the periodon;r;im i< :5.'_'7 to i i< in all prolialiility a 
true cycle. The douiit that exist< is due to i he smalliie.ss 
of the I'atio and the few recurrences only two- — • 

' ■|'lai>I( : : "'I'lic I'r-iiiiliinraiii of .Mniiiiclir iJcclinal H'H." ]•]'■ l-J- 
12."). 

-■{"Iiii-c uliii (Icprccatc ilic u~c of >\icli meaner data >li(iu'il con- 
>ii|rr well the testimony of l.did Kch in licforo the Mctcordlotiical 
( 'iilnmitttr (if the l!(i\al Society. lS7(i. 

(Question 1710. "Tlie >illiL wliieli pallialnelLf will (live for tiii-f 
|)ur|iose lieiiiij, a liiiiiteil -uiii. do you think that it wotild lie well to 
l-edlice the Iiuiiiliel' of ol i-er\ at iolis ill oldef to ha\'e more money to 
s|i(iiil Upon the reduetion of oli>ei\ ation>'.' / Uniil: nt nil i r, hl.< iiiilil 
(iiii ill nil i/iiir-s jiiiiiiil, Ihi >iiii sjtiil III mill, /.< n.ui jiU li il . it innilil In- 
irrniii/ III inliirt llii iniitiliir (>\ nh.Hll'iltliiii''. 

(Question IT.i.'). ••Siipposiiii: that yon had oi f thcM' .analyses 

calculated for a peiiod of II >(\-iis. would each year's oii.~ei\ at ions 
and >till more each period of 11 years oliservtuions, re(iuire to bp 
introduced into this analysis so that yon would lia\i' an aniily.-^is of 
22 vears, and an aiiaK ~i- of .'vi .\-ear>, atid so on finiii time to time, 



20 



i'.nnioniic Ci/rlrs: Thtir Law and Cduse 



that our (lata atVoni. A prater (■(mfidnicc in the cxist- 
vnvv of ;i real pcriitd .,f ;{;{ ycar< is friv,.„ |,y th,. fad tlial 
Hnickncr ' claiins to have UmvA a true jxwind ,,f al.out 
■'<■") years in an cxaininafion ,,r a vast mass .if rainfall 
material all over the world. Accordingly, the (-xlstoncc 
ill the Ohio \alley .,f a r. al :{.{ years p.^ri,,,! ,,f rainfall we 
.shall assume to he very prohaiile. 

'i'he other two periods of •_",) years and 'M) years are 
not easily disponed of. j^ui ,, the fn'st place, the ratios 
of thes(iiiaresof th<' respect ive amplitudes to the mean 
square am!)li;ude of the periodojiram are not such as to 
justify the acceptanc", with any deirree of confidence, of 
the exi.vt.'iHv of tru( cycles (.f 21) years and :M\ years. 
In the sec,,nd place, diey ;ire hotli so cIo..,. to the period 
of .T5 ye.-irs as to cau e a (loul)t as to wlu'ther they may 
not he spurious p<.ri( ds that are likely to appear in the 
neighliorhood of a real period. ' 

Considering th.' sn.,rt raiifr,. .,f ,,ur .lata it woidd n.^t 
l)e prop.'rly cauti..us to pivss the point <.f th.' exi-^ten.'.. 
of any .l,.|init<. r.>al .•y.l... Hut tliis nuich is crtain: 
If there are tru.' .■y.'h-s in th.' data ..f th.' 72 years .)f 
rainfall in th,' ()hi<. N'all.'y. th.'r.' i. far ur...'it."'r jiroh- 
al)ility that tw.. .'ydcs ar.' tho^,. ,,f s y.'ai,^ and l^.'i 
years than of any .ither round numhers Ix'tw.'.-n :\ an.l 

or, hciuK 'lone, V'oul.l it he done eiur f,,r ;,ir' / ,.„„,,„/ .«,y uhdhn- 
amithw'j irdh reference to Terrcslriai M,UoroU,gy {, done once for oil. 
I l/nnk probably the work vill ncrcr he done." 

' Efiuani Bruckner: Ktima.'^clnrankungeH scit 1700. Bruckner's 
period Jluctuiitcs greatly in length and l,as an avcrac' value ef 35 
years. 

'SOmster: "The Pcri,Hh,grain ,.f .Magu, ii,' D.rlinatioi,,- p. ],m. 



I 



('ij(l( ■■< iij h'duifdll 



21 



3r» yc;irs. Morcnvcr. the periods of S years aiui -Vi 
years alfurd tlie iii(»l i)n)l)al)le basis derivalile fnnii t!ie 
(lata up'iii whicli tn rea-nii I.Mth as to ttie future enur-e 
of rainfall in the ( )irKi \ alley and as to the courM- ol the 
|)heiioiiiena dependent upon rauitall. 

A->uniinti;. tiien, that lor the i>ur|)o>e in hand, the 'S.\ 
years aiul S years periods are the ino>t proliaiile and 
valuable, we t\irn to the (•on>ideration of the e(iuation 
to the t;rapli niviny; the course of rainfall in thi^ Ohio 
\alley. 

Tin I'Jiuiiliiiii to till- Udiiif'iJI Curve 

It will !)e helpful to apiiroaeh the alm'braic de-erip- 
tion of the cyclical nioveinent of rainfall in the Ohio 
\alley, l>y observing Imw we oiitain an increasingly 
a<'cin-ate account of the actual rainfall by superpo>infi; 
tlie constituent cycles. We shall ii-e. as an index of the 
relaliv(> lit of the several ciu'ves, the root-inean-sciuare 
deviation of the observations from each cur\-e. 

if, as a preliininaiA step, the raw data of the course 
of aiuuial rainfall are examined, it i< found that the 
mean aiuiua! rainfall in the Ohio \'alley is -n.l'.l inches, 
and the root-meaii-xiuare deviation about the mean i.s 
N -=- Ci.TD inches. 

if the lonti; '.V-\ years cycle is con>idered Iry it>elf. it 

ajip'^ars that the idot-mean-><iuare de\iation abnut the 

'.K.\ years curve is .S'=b.:5!> inches. 'I'he ^r.aph of the 

.S;} years cycle is ^i\-en in iMjiure 4. Its enuatiou is 

■ >_ \ 

(/ - 41.1',) + 2.88 sin T ^ / - li-V 7' j, 



II 



it 



ill 



22 h'.niiiiiniir Ciirlis: 'I'hiir l.nii- <nn/ ('hum; 

"> 1 1 ' 1 ' ' ' I I 1 1 • 1 T— Ij 



= I- 

3 o 



is* 

I 5 

"^ + 



Cljrlrs nf ffdinfiill 



23 



till' nritiiii hciiim :it \s:V.\. 'I'lii- riir\r trans in l.old 
oulliiH' IIk* p'ucral ((Mir-c of ramtall. It m;ivi'-. tlif 
tfiiiuiiil--\vi'll (il tlic laiiilali iiiii\ tiii'iit. 

If the S vears cycle is Mi|>cr|iii-ci| ii|iiin the 'X^ years 
CVcle, the root -iiicaii-><iuare tlevialiMn aKmit the ciir\t' 
liecoiiies ,S .").(Ki inche-. 'The fira|ih of i he cnriihiiiat imi 
.if thcM! two curves i.^ traced iti ! ijiure "). Its ecuiatioii is 

v = 4i.i<> + 2.s,s>iii(~.'J<+328»7') . 4.i:<^in("[^''/ : ;n(t"!r), 

tlie(Miy:inl)eiiiK!it 1S:?0. A pniiit of iiiten-t with re^jard 
III the lliiw nf the curve i- the ia|)idity with which it 
ri-e> friiii' the Ica-t iiiiiunium to the ^realevt inaxiiiumi, 
and the ^lnuiie-s with which it then descends to tht; 
-iili-eiiucnt lea-t niiniinuni. 

If tho 8 veins c\cle and its .seiniharinnnic of 4 yi'ars 
are cniiiliined with the IV.i years c\r|e and its ^eini- 
harinoni<' of Hi..") year-, the root-ineanMiuare deviation 
aliout the coinixiuud ciirxc lieconics N .").'_*'.» inche-. 
riie p:ia|)li of the curve is ^ivcn in i i^iure tl. Its eiiua- 
I ion is 

// . H.Ut f 2.S.Ssin(^' t + 328° t) ^ 2 /-'.-.MnQ^^ ^ 271' 42) 

+ 4,i:>sin("^/ h:{10=4r) +-2.1}si.(''/ • 1S()'2S'). 

tho origin liein^ at ISI^i*. In tliis clo-er approximation 
the characteristic rai)id rise to ii general luaxiinuin and 
slow fall to ii gemi-:vl iniiiimum is r('i)roduced. Another 
characteristie is tlie longer interval that the curve 



2-1 I-'.rouitihir Ciid, s: Tliiirl.ti.i und di 



use 




11 



-? 



■Z ,Sf 

i 2 ^ 



\4 Z 

a ~ 



? =5 



i + 



f Si 



( j/clts iij h'diiijdll 



26 



A 



JS|» 






c o 

i: ?^ 

.£ N ■ X 

JS CI I 

S -*' 



» :£ 









.a 

Ml 












? - 

u 






+ 



f l! 



frfyA// w //^uipj jPOuu^ 



26 



/''roiininii- Ci/rlis: Tlitir Luir nml ('aiisr 



linfi(>rs at the niiniiiia and the sliort period during which 
it flows in the iicighlxirhood of tlic maxima.' 

HdliifitU III the Corn Hill 
Tlius far \Vf liavc dealt with the law of rainfall oidy 
in the Ohio \alley. The ()l)j(>et in taking the Ohio 
data, rathei' than the data of a state more rej)resenta- 
tive ot the leading cei-eal an\i, was to tuake an investiga- 
tion of a longer meteoiologieal nM'ord than is afforded 
l)y the data of the centi'al Mississi|)[)i N'allev. liut our 
purpose in dealing with meteorologi"al records at all is 
to >ho\\ the dependence of crops upon th(> cyclical 
mo\-einent of th(> elt>ments of th(> wejither. We must, 
tlierefore, prove that the cycles of r;iinfall which we have 

' I .slii.uid like l(j iiuikc clear llic inctlmd j |,a\(. fdllourd in the 
derivation of the equations to the eiirves. My ol.jrct was to obtain 
a suinniary drscriiitioii of the jreiieral c<iurse of rainfall in order that 
I iniKht di> .ver, later on. viKtlier tlie cJiai^K-teiistic general fea- 
tures of the movement of rainfall are rei.rndue((l in the el,anf;in(i 
yield per acre of ihe ero|is. .\.-. a tir-l sn>|, I tried l;. di teet the real 
cycles in rainfall and I believe I have shown thai, if the 72 years 
record is suiiieieiitly loni; to reveal the true eyeles, then the most 
probabli' lentrths of the cNcles are, in round numbers, ;{;i years and 
S years rcsjieetively. With so short a raiiRe of data I regarded it as 
u.seless to attempt to calculate the li.njrths of the periods t(. ;i f;r(>ater 
(leRreeof i)reei.sioii. 1 next h;id to derive the eiiuations to the curves 
shouinn the eharacterisl ic j;eneral course of rainfall, and it seemed 
to me that, for this imrpose, the method described in the text for 
evaluatiiif; the c(]ellieients in a Fourier .-series mitrht iir()p(>rly he 
ll.'ied. If the ;« years cycle were taken as thi. fundamental eyelp, 
then the S years cycle would be api)roximately the fouiih hannonic 
in the series, and the 4 years cycle would be the eishtli harmonic. 

The arithmetical |iroee.s'< for eomimtiiig the coefficients i- indi- 
cated by Profe.s.sor Scluister in //(,/,/, „ ['criodicitieK, pp. 13, 14 and is 
briefly desoritx-d by Professor Perry in an article on "TTarmf)nic 
Analysis" in The Elictricwn, for Fehrunrv .'), 18it2. 



fhi 



( ■//(;/(>■ ^^J' limiifdll 



27 



discovered for the Ohio \':ill(\v aro likewise the eycles 
tlint exist in the lieart of tli" tirain pnuhieinj; area. 

Amoiifi the states of tlie Middle West, Illinois is 
probal'ly the most liigidy representative of American 
cerea' prodi'.etion. it i)rodu('es the larfjest crop of 
corn,' which is tlie leading American cereal, and it 
ranks second iii the prixluction of oats. Most of the 
otluT cereals that are |)roduc<'d in tlie upper Mi.sissippi 
Valley are likewise cultivated with succos in Illinois. 
Another fact th.Mt maki^s Illinois a desiralik' state for 
our i)urpose is that its meteorological records are fairly 
lonti and are ol)tainal)!e from so many stations as to ho 
representative of the weatlier conditions in ti\e entire 
state. This Inst fact is all-imitortant if the statistics 
for crop production of tlie wlioie stat(> are to !)e con- 
sitiered in relation to the weather cycles of the state. 

In 'rai>le 111 of the Ai)iiendi.\ tii tliis chapter the 
recoi'd of tlie annual rainfall in Illinois i- ^iven for a 
period of U years.- The ideal direct method with 



' This slatciiK'iit w;i.s accurate when it was first written, Jiut in 
l'.)l_' Iowa piined i)y a narrow inartjin tlie tii'st place anuniK tiie cdrn 
jiroilucinf!; states. 

■Tlie raw data were taken from BulUtui 11' of the Weather Bu- 
reau of the I'liiied States and from the Annmtl Hi /nuts uf the C'l\if>^ 
(if the Weatlier Bureau. The stations used in eoniputinn the r.eun 
annual rainfall were; In Xortliern Illinois; Aurora, Canihrii, 
Chicago, Ti.skilwa. (laha, Kishwaukee. Ottaw.-i, \\'iiiiiel)af;o, aiul 
Henry. In Central Illinois; (hark'ston, ( 'arliii\ ille, Coatshurn, 
Decatur, ( !rint;s\ille, Knowille, IIa\ana, I.allarpe, Pan.;, I'eoria, 
and Sprinfjfield, In Southern Illinois: Cairo, Cohden, Carlyle, 
(iolconda. l-'lora, Ciii n\ille, MeI.eanshoro. Mascout.ali, Mt. 
Caniiel, and Pales) ilii . 

All of these ..-tations do not iiresent full records foi- the 41 years, 



28 



/• 



CDiioinii 



Ci/clr.'^: Thiir J.mr <uiil ('(in.se 



reference lo these data wnuld ' to rotiiptite ihp 
])(>ri()(l()^raiii in the same iiuumer in whieli it was eom- 
ixited in the e;iso of the Olno Valley data, and then com- 
pare the periodo^rams. l<nt this mctliod has not heen 
tiillowed. A lc>s tlirect, and far less lal><)riiius, prueess 
has heen adopted. \\'e know fiom the Ohio (l.ita that 
there are two cycles of rainfall, a IV.i years cycle and an S 
years cycle, and wo. know, fnrthermore, that wh(>n the 
curve for rainfall in the Ohio \all(\v is computed for the 
'A'.i years and 8 years periods Jind th(>ir s(Mnih;irnionics, u 
good fit to the data is obtained. 'I'lu' (luestions that are 
Jisked with reference to the Illinois data an- these: 
If W(> assume the oxistence of a IV,^ years |)eriod and an 
8 years p(>riod in the Illinois rainfall data, will the 
rainfall curve fit the Illinois data as well as the Ohio 
curve fits the Ohio data? Will th" Illinois cur\(> re- 
produce the characteristic features of the Oiiio cur\-e'.' 
A pr(^s\nnption in faxor of an aflirmative answer to 
these (luestions is sup;Kest(Ml by the fact that the correla- 
tion between tlie amnial rainfall in. the Ohio \ alley and 
the anmial rainfall in the state of Illinois is /•=().()(). 
The jiraph of \\w, curve of rainfall in Illinois is given 
in figure 7. Itse(iuation is 

// = .S8.5:H.S.(« sin (~^^^;V2.-,'' :{,-)') + 1.87sin(:J^/ f IW^Sa') 

+;i.O.-)sin(''J'/ f 2}r5_>j -r 1.12 sin ('j" / + 2:<2° 2t;), 

the origin being at 1870. The root-n.ean-siiuare d(>via- 

l)iit ill tK) yrar were fcw.-r tluui scvt'ii records obtainable while for u 
large proportion of the yeans the tliirty records were conii)letc. 



Cycles iij Ji'fiinjall 



29 




+ 



+ 



If 5 



4- I^ 



2 -- - 

^ . b loo 
1^ r \ y; 



+ 



^ 



sSLj:>ui uf ii0^u:ej jDnuu^ 



1= ' ^ 



+ 



II 



( 



30 l:<niiiifnir ('ijclrs Tin ir l.dir <niil ('au 



.sc 



II of the ()l)S('r\;if idiis fmin tlii- curN*' is ^ = \:l{). [n 
cast' of tho Oliid ciirNt' thr rnot-tii(>;ui-s(iiiar(' (Icxialitm 
was .S = ").2<). Hut thi^ i- a l,|.ttcr relative lit tm- tlie 
Flliiini- curxc ilian we liavc a v\\i}\\ to ( laiiii. Iiccau-c in 
' Miio the mean annual rainlall i- M.I'.t. wliijc in Illinois 
fli.' mean is AS.7,:\. U we cxpivs- the relative M'atter of 
the oli-er\alions aliout the euf\-e a< thi" ratio of the 
root-niean-s({Uai-e deviation of the ohser\at ion< to the 
mean rainfall, we ^et lor Ohio ami Illinois, resi)ectively, 
S' .iL'Si.S'i -.KM), 

In I'iiiure s, the Ohio lairve for 1S7() JUKI is placed 
upon the sinie r'haH as the Illinois curve tor the sain(> 
li"\\ of tini.', and the derive of cotrespondeiice of tiie 
two (Mirves i> >een to he >o clo^' that, with due allcwaiice 
hir the difference in their inean annual rainfall, they 
^eem to he ahiio-t coiiMi-ucnt . 

We may ->ay. thetvlore. that the two curves fit their 
re.-i)ecii\e(iata e(iually well. 



<*nr prol.leiH ha- now receiv -d it> solution. Amuial 
ramlall m the chief jiram-prodinanti area of the Cnited 
>tate- ha> no >ecular trend, hut it- mean course is the 
re-iiltant of caii.-e- [irodiicinii two cycle- of 'X\ years 
an<l S year> re.-pectiwly. Th,. niani,( r in which these 
'•ycles of rainfall i);-oduce a rhythmical e.xpan.-ioii and 
<'"""•;!'•' i"" ill the yield of the crops we AvA\ exauiiue in 
the next chapter. 



Ci/rlrs of RdhifiiU 



31 




Sicfiui ui //e^uiej /enuu^ 



; ■ t 

f ■■ ■ ■;. 



:i2 



Kcmonnc Cycles: Thnr Lu,r an<l Cntse 



APPKXDIX 



TAIil.i: I. Annlai. ({umm.,. ,v nn 
Stations: Cincinnah, \\,n 



'"'in \'\I.I.KV 
l>-MOI Til, .M.,|[||.;|T\ 




Cycles of R(i in/all 



M 



'lAIU.!'] II Tin: PKTUnnrxatAM hf Hmnkm.t. i\ rin: <>i:im 

\'\I.I.KV 



y = F(t) = Ao + ai vm kt + bi sin kl = .U + .4, sin ik-t ■ r 



LeWQTH 








I.ENdTll 


1 




or 

PCRIOU 


1 


b" 


«- W -4* 


or Pe- 
riod IN 


a« 


b'- a'i-h'.i 


IK Yeaiui 








YE.tIM 






:< 


! itl-.'S 


•2 }S21 


1 .'i 711!) 


21 


.()()4fi 


4 12110 1 -1 i:i(Ml 


4 


.(HK):{ 


J r)tis!) 


\ 4..',f,i»2 


22 


.24.-,! 


2 I2:i7 


i 2 til, ill 


a 


.ositr 


. I.'")2() 


..-)417 


23 1 .8471 


.N711 


1 1 71s,-) 


(i 


. 2221) 


. 1 1():{ 


..•it'.2:i 


24 .:m\ 


.(H17S 


. 422! » 


1 


2. is;{s 


:f 7s(;(» 


r, !»707 


2.-) . 27.^).-) 


.1327 


. 40S2 


s 


!» S21.". 


7 .'.")ii.! 


17.077S 


20 .()-)()(> 


.(HH)2 


.(l.ll.S 


'.) 


U.TJ7 


:{l2i) 


•{117 


27 .!»r.()2 


.IMII!I 


.11711 


ID 


,."i!t7s 


Ol'.ll) 


.(iltLS 


28 .1)227 


.0.300 


.11.""! 2 7 


11 


1 .(l7.Vi 


(i71)I 


1.7.-) 17 


29 4.2t),-)7 


1 ll.-)3 


.-) 3S10 


i J 


. I-U 1 


11 1:{ 


. .-..-) 1 t 


.•^0 .tUtM 


. 17.17 


1 i2.;i 


l:f 


.(H)ll 


(HHI7 


.(HTil 


:n 


6112 


..-)'. >23 


1 20:;.-) 


11 


. I07S 


11170 


.274-. 


.■i2 


. •-)776 


1 llllS 


1 li'.ilt 


i:, 


IS7I 


OSIiii 


27:!7 


33 


2.31!)(» 


-) '.1071 


.s 3173 


Hi 


VtiiU 


OIJI 


Ml.-) 


34 


.2017 


1 7tl.V2 


1 !H)tl'.) 


17 


l»7!t."i 


m->i) 


10421 


3.-) 


.04.-)i) 


1 7!il I 


1 S370 


Is 
1') 


1 (777 


'.•270 
1 '.1122 
1 .Vim 


3.,Sti02 
:i 41'.l'.t 
1 (>25-) 


36 


.0036 


6 M.-)67 


6.stlo:{ 


•JO 


II.". II 


Mean v.iliic < 


f .1- = 2..-)!.-)!) 



r 


: 


kv' 








iUi 



;i4 



hcuiuunic Vjirlrs: Th, ir l.,tw „,„/ ( 'nnxt 



TAHIi: III Vsx, „,,;,„,.,,,, „ ,,,,_,^,„^ 



Year 



1870 

1H71 

1S72 

IS7:! 

I.S7I 

ls7.-. 

lS7ti 

1S77 

1.S78 

1S7!1 

lS.si> 

|S>>1 

l.sM 
1885 

INSS 
INNO 
1S<»0 



Rai.nhh. in In,,(k« 
'JO (1.-) 

:« its 

11 f.L' 

.•:.' !M 
Ml :;i 
I.". .-,1) 

12 7(i 
37. til 
3ii 10 
42 :il 
42 ;i2 
4<».0t 
47. M 
1.-.s;i 

l(» SI) 

;i(i Hi 
;« to 
:!'.» 41 
3(i.2r 

40 .il 



Ve.\8 



I. so I 
lHi»2 
ISiW 
1.S94 

is!»r, 

IV.Mi 

is;»7 

I Si IS 
I.S'M) 
1!I00 
KMII 

I 'Ml.' 

I'.Ki:; 
I'll 1 1 
I'm:, 
I'lm; 
I'.io: 

I III Is 
I! II I' I 
Mill) 



RAI.VrALL IN InvhIM 



•■il 


u 


II 


17 


a.-) 


.,S!» 


28 


.00 


.•<2 


.02 


.■{S 


27 


.■(7 


It 


I'l 


nil 


;ii 


'<"> 


;i(i 


I'l 
17 


■12 


ii."i 
07 


:w.33 


37. 


33 


3S. 


10 


Ill 


il 


II 


"1 


.i 1 . . 


U 


:{s , . 


'i.'i 




J 



(■iiAi'ii;i{ III 

liAIMAI.I, \\|) llll Cliol's 

•■Ft i-; iinT<' uv;ii||,T 'loiin;;,!,,! uiHloi,i._r „i,|„,iit nn!" 

- -Wll.l.l \M .I.WIKS. 

Tx the pivccdinir clmptcr fli," cniirM' of ;innii:il rainfall 
in the til-cat (•(•rcai-|)iu(liiciii<r area of the rnitcd Slates 
has iiccii shown Id \u<>\v in cycles: Tlicrc i> a lirouiui- 
swoll (if 1hirt\-tinv(' y«>ars in Icnjith upon which cycles 
nf cinhl y<vir- in .hifation afo supcriioscii. Our ol),i('ct 
in studyinti- the rhythmic chanties in the \ ojunie of rain- 
hill was to iiiinj; ihe.-c clian^res im,, rejalion with th(i 
variations in the yield per acre of the crops, and in the 
proseiit chapter we shall lie al.le to realize our purpose. 
The actual course <,f the \aryiiiij: yield per acre of the 
crops will he shown to have Ix.ih a secular and a cyclical 
inovenient: these two inovenient> will he separated for 
reiu-esentative crops; and tlie cyclical movements will 
1)0 shown to he dependent upon the cyclical iuov<'meuts 
in the weather rej)resented hy the cycles of rainfall. 

The Srndar 'I'n ti<l in tin Y iibl of ///« ('n)p:< 

The state of Illinois wa> clios(>n in the i)recedinp; 
••hapter to illustrate the jrcneral conditions of rainfall 
in the Corn Helt of the Middle West, and we shall now 
examine the statistics of the yield of its most iini)ortaut 
crops. 

35 



;<(i 



r.cnmmuc Cijrirs: Tin,,- l.„,r an,/ Cms, 



A^n.ult,,.,- f,,r I'ML'. urr„HltlH-...r,-,.aK.-an.l valur of 



^lllilniiK'd 



Amika.,1. am, \u.ik o^ Cu,,,.. ,.v |,,,.is,„^ pn^ 



< mp 
(IM orii 

(2) Oats 

(3) Hay 

(4) \Vli,>at 
(o) I'otatiics 

(6) Harlcv 

(7) Hy,. 

(8) liiickulicat 
(!»' TnLacc, 



Acreage 
l'».ti.")^. ()()() 
l.JJd.dOO 
-',.') IJ.OOO 

I, l.s:5, ()()() 

i:<7.()()() 

.')7, ()<)() 

is.ooo 

l.ooo 



\'.-||llrii|' ( 'rop 

S17}, 7!) 1, ()()() 

.')1,.S is, 0(1(1 

4 l.loL', ()()() 

S. til 1.(100 

N.:{o.',ooo 

!i:,2.0(K) 
').'W,000 

70,000 
(IJ.OOO 



It is clear, lV.„n tlu^ Tal.I,., th;,( tivc crops c.rn, oats, 
huy. wheat, and p.,tat.,(.s make up the l.ulk of tho 
('r(.])s ,,f lUii.ow, and one muld n..l ^o far \vro„^r if }„. 
based his ^^enerahzatioiis as P. the eonditioiis of a-rie(il- 
tiire in the st.nte uix-n the.s.- Iiv(> (to|)s, Hut for the 
I)(iri)oses we have in view, in this and other chapters, it 
is not pos.il.Ie to utihxe the statistics of wh<.at pn.duc- 
tion l.ecaioe hoth spring and winter wheat are ^Toun in 
t\u- state, and th.- stati.stics of th(-ir relative yi.-ld and 
price an not ^iven in th.' pulilisl,,.,! n.at.Tial for the 
lon^r r<.c,,nl cov.'r...! in our inv.-stitration, .Vccordingly, 
the cn.ps that hav.' he.-n a.'tu.aliy use.l in our inquiry 
are corn, oats, hay. and [.otatoes. Th.>se .Tops p.tid 
m.r.i per cent, of th.> croj) acn-a^e and !Jt).4r) per cent, of 
the crof) value a.s the.se .luantities are yiven in the above 
Table. 



J 



Ruin fall ii:i<l Ih, ( 'ntjia 



r, 



A- ihr yield JUT aciv (if llir van.ni> cnip-. mav <Iim\v a 
secular a> well a-> a <'uini.|r\ cydiral cliatinc, it will l)(. 
nrrcs-ary, l.ctnrr their <'yclical eleinents ca.i he hmuulit 
into relation with tlie CMrre^potKlinir cycjieal clKinire^ of 
niiiifall, to eliiiiiiiate tmni the recorded course of the 
yield per acre of the >e\eral crop- the el.'iuetit of chuiiKe 
that is secular ui character. 

I"he method that ha~ lieeri adopted here to elTect the 
clitiiuiatioH of the -ecular change i- -imple, hut to se.'uro 
a hrst approximation, it is ade(|uate. I'or a period of 
time covered hy the -talistics a chaii^r,. is reKarde(l as :i 
secailar change if. lor the period of time taken as a 
whole, the yield per acre of the crop shows a tendency 
• ■ither to increase or to (lecrea<e. in order to deternune 
whether there is a secular chanK(> in the yield ner acre, 
for a certain period of time, the yield data are correlated 
with time, and the exisfencc or non-existence of a 
secular change is inferred fnun the relative magnitudes 
of the coeflicient of correlation and its prohahle error. 
It there he a seculat change, the calculation of the 
coefficient of correlation of the yield with time is then a 
first-step toward the elimination of the secular element 
l>y means of a n'^rcssion eiiuation in which the co- 
efficient of correlation is a factor. 

The method may he illustrated hy taking the history 
of the yield per acre of corn. In Figure <) the actual 
yield per acre in Illinois is plotted for the period 1870- 
I!»l(). The straight line showing the secular trend of the 
yield is tlie graph of the regression eiiuation between 
the yield per acre and time. The correlation of the 



.'<^ Economic I'j/clt'n: Th< ir Lmr imtl Cnunr 



-\ r 




-I 



S •- 





O 


.a 


5i 





*•• 


1 


09 


c 


O 

'Si 


c 




8 


o 






o 


C<5 


V 


a> 




f.-i 


a 


C'^ 




+ 



^5 



i II 



_ "3 
C S 






jjjp jgd uiOD ^o s/^i^snp 



UdinfiiH III ■/ th, I itijis 



;{!t 



yield per awe lunl time is r = .3H'J^ .(I'.mi, ami llir rr^ro- 
sion e(iu.itiiiii is, </ = .2(Mj-f-2(».'.»;{, where !j= \ hM pn- 
acre, .r limr. arid the urifiin i- at ISTO. TIic -n iilar 
tr-ciHJ i- (•liiniiialcil liy mean- cii' llic laiM- -iiiiiiii;,, i/rd 
in llic rcnit---inii f(|iia' inii : I'.itiiiinint; vvitli the year 
1^7(1, a< many time- .'JOl ate -uKl racicd fmni th(> 
yield per acre tor tlir ~c\rial \rai-s, a- tlic ic^pcrl i\-(' 
year- dillVr trnm |s7(». i m- (Aamidr, itic yii^ld tm- ihc 
year ls7'_' was :{•)., S iiu-ln'i- ncr ari-c; (•Mii-(.(|nriit l\ ilic 
rcdiicid >icld fur llial year was ;{'.». S lii .204) - ii'.t.s 
. lOS ;!ll.:'.ll. I muic 10 iraccs ttic yield per acre of cnrn 
freed tVnin tlic -ccidai- Irend. 

''I ln' I'l'iu' leading cMip- uf IllinMi- that Imiim llie 
l)a>is iif uuf inxc-t iiiat iun. nnly i\\m. cirn ami pntaiMC-. 
sIkiu a >i^nilirant ' Icndcni-y id -riMilai' I'lianuc. Tlie 
ciii-ii'lation iietwci'ii tlii' yield per aeie and time is, 
for hay, /• .ill:;±.lo:) and, tm- nat-. r .(i i:^ -t . lo.-,; 
(••iiwciincntly the tiuuic- I'ni- the yiejil pel- acre (if tlie-e 
t\V(P ei'iips ha\e lint heen I'eiliii'eil. In the ea>e n|' 
potaliies. ;■ - .i2'J±.10L .and the re;ire--'.iin e(iii;iti(in 
is !/ = .2;i.'{.r + 7o,.")l , where the oriy:in i- ;it ls7il, TIk' 
fimiiTs for the ai'lual ,\ ield per acre and t' icdui-ed 
yield jier .a. -re for corn and potatoe-, as well .a- the 
li<iures for the yield of h;iy and of oats, are fi'ven " in 
'l"al)k' 1 of the Appendix to thi> chaplcM'. 

' Tiic imlicatcd secular trciul in iietaldcs is not .'^ipiificaiit in 
the iiuitliciuatical sense, Ijccaiisc the i)nibai)lo error of the cocfliciciit 
of corivlatidii is nearly as larf;,. as the coefficient itself. I have 
neverthelr^s cliniinatcil the imlicatcii srcular trmij licfcire iisiti^ the 
(hita. 

- Tlie raw ihtta urrc taken from linUilins .')(), .'iS, (;_>, {):', of the 



40 h'ciinoi/iii Ci/rlcs: Tin ir Lmc itnil Cans 



\i. c3 






'y \ '^ 

3jje jjd ujoj ^o ^f3i^ <,nn 



h'dinj'dll (I'll Ihc Crap.i 



41 



Cnliciil I'iriotis Of (irtnrlh 

If the liiytliiiiical cliaii^cs in i-aiiit'all arc to ^,'i\i) the 
(•lu(> to the clianfics in the yield of tlic croijs, the vuria- 
tions in the rainfall inu>t lie closely related with, the 
variations in the yield of the crop>. l^ut diffcreut eroi)s 
ha\-e dilTcrc nt times of planting and of harv(>sting, 
different pci-ioils of jirowth. and diffci'cnt rc(iuirenients 
of n.oistini a't the vaiioiis staucs of growth. Th(> direct 
way to find whether the eoui'sc of rainfall det(>rinines 
the conrsc of the \ar_\int!: yield of the crops is first to 
ascertain the ci-ilical season for every crop: and then to 
conipai'e the course of the yield of each crop with the 
course of the rainfall of its critical season. 

'l"he nielhod of discoverinfi the critical period of a. 
crop may he illusti-ated in the treaiment of corn. In 
'I'ahle II of the Apjicndix to thi- chapter, the mean' 
monthly rainfall foi' Illinois is tahulated for seven 
months, March, \piil. May, June, July, August, and 
Septemher. Talile I of the Ap|)endi\ records tlie data 

I'.iircaii (if .■<tati>tics ■!' the liiitcii Slates l)('| artriiiiit c.f Ai:i iculture 
and fnini icrriit )'iiiiIi,hi/:s of Utr fiiitnl .^tates ] h'l'arljiiciit cf 
Aiii'iciiiturc. 

' 'I'lir raw (lata unv lakiii frdin l!n'!,liii \\ ,,f thf Weather 
Hie'cau of ihe \'n'iU'i\ States and fiiini the Animal li'i j,orl.-< of ilie 
( 'hief i.f tiie We.allier ISure.au. 'I'lie sta'ions n-r.l in ci.niimtirif; tlio 
niean ni.intliiv lainfall ueiv, in .Nniilirrn Illiiii,i-: Aurnra, Cain- 
liiiilire, Cliii'ai.'o, Ti-lxiiwa, (laiva, Kishuauisee, ditawa, WinnehaKO 
and Henry. In ( eninil lilimris: ( 'liailesion. ('ariin\ilie, Cdatshurg, 
Decatur, Cri-ifji-ville. Kn(i-\ille, Havana, I.allarne, I'a'ia, Peoria 
and Sprinu'tield, In Smitliern illiriei-: Cairo, Colul n, Carlylc, 
<;ole,,i„la, {■lo',., <;rren\i||(, Mel.ean.-lioro, Mascoutali, Mt. 
* ainii 1 ami l'ale>tine. 



I 



r 



1 In 



i 



i 



42 



F.ciiiii»)iiv CycU-H: 'I'Inir Ldir and ('mtsc 



rrforrinp; to the yield ])vv ticrv of the scvcM'nl crops a. or 
the secular tfci.ds have hccii (>liiiiiiiatc(l. These , ao 
Tallies furnish the statistical material for ascerta.niiiK 
the critical periods of the respecti\(> crops. The facts 
us to the times of plautinu; and harvest iuij; may ho 
obtained from au article in the Yon-hiiol: of the I'nited 
States Department of Agriculture, 1!)1(), pp. 4SS-4i)4, 
on "Seedtime and Harvest: .\v(M-afz;e Dates of Planting; 
and IIarv(>stinfi; in the Tnited Slates." Th(> method of 
detoctinji the period of ciitical relation between yield 
and rainfall consists in ascertaininfjj, for (>ach croi), the 
month or combination of months, within the intei\al 
between planting- and har\(\stinp;,' whose rainfall j^ives 
the liifihest correlation witli the ultimate yield ])(>•• 
aero of tho croj). The tim(> for planting corn in Illinois, 
aocordinjr to the ofiicial i)ul)lication cited abov(\ bc-rrins 
about .\.i)ril :?(), it is soueral about May 13. and it ends 
about June 2. The avorap;o time for harv'stiiifj;, accord- 
ing to the same publication, begins aliout September "_'(), 
is fieneral by October 2'.l, and (Mids ;iooul Decemlier 10. 
The correlation lietween lh(> yield of corn per aero 
(secular trend eliminatedi. and the rainfall for June is, 
r=()()'l: for July, r = .l'.»('.: for .\u}iust. r .2'.i;5; for 
8ept(>mber, r=--.(»S7: for .iuly and \uKust combinod, 
r = .5S(). TIh- critical jieriod of growth for coi-n has, 
therefore, beeti assumed to be the inter\al ■>i two 
n:')nths .Iuly and .\un-ust.- 



' I'l.r .-iinic |)urp(j.-c> it wouM he (lf>ii:il,|i' ti> tc.>t llic ('iirrrl;iti(iii 
licyiiiiil tlirsc limits. 

•Of ruiir^c ail i>()^>ililr cuiiiliiiial inns nf iiKiuths have iml hvvu 



Rdiiijiill and the Crops 



43 



The critical periods for the (»ther crops are, for oats — 
May, .lune, .Inly, r = .2',tO; for hay March, April, 
May, ,Iuue, /• = .<t'2(); for potatoes -,hily and August, 
r = .()()(). The critical season for corn, us we found a 
while a^o, is .July and Aiifz;ust, r = ..W.). 

The hish correlation hetween the yield of tlu" crops 
and the rainfall of their respective critical seasons 
promises well for the theory as to the rt^lation of the 
cycles of rainfall and cycles of crops. In the last chapter 
we fcund that hy ('xaniininp; the periodograni of annual 
rainfall in the Ohio Valley, cycles of eight years and of 
thirty-three years were discovered; and that hy taking 
periods of thirty-three years and eight years with their 
seniihannonics, a good fit to the annual rainfall curve 
was ohtaiued. It was then shown that the aiuuial rain- 
fall in Illinois is correlated with the annual rainfall 
in the Ohio Valley, the correlation coeflicient being 
r = .(iOO. Upon the basis of this relatively high correla- 
tion, it was assumed that the animal rainfall in Illinois 
pass"d through similar cycles to the rainfall in the 
Ohio Valley, and we found that this assumption was 
justified by the facts inasnuich as the hannonic analysis 
api)lied in th(> same way to the Illinois data afforded as 
good a fit as when it was applied to the data of the 
Ohio Valley. Since in two of the four representative 
crops the correlation between the yield and the rainfall 

cxliaiislcd in the hIjcivc caM , iKir lia\(' we iiiadc any alt('ln|il to 
place the ci'i'.ii:!] |)criii(i for a .■^mailer intcrNal of lime lliaii a niolitli. 
If for any iiIIi't [nTJoii a closer relation could he found than r — IyS9, 
the conclii.sions that \\v diuw from our investigation would only he 
.streiifithened. 



It il 
• ii 



44 l-'.i-iiiioinic Ci/rlis: Tin ir l.inr (uiil Cuiisc 

111 the ciiticiil s(>;isoTi of "rnnvth is y.rc;itcr tluin tli(> 
(•orrcliilidii liclwccii llir .■iiiiukiI •-liiitall in llliiinis aiul 
tl"' aiiiiiKil i;iiat;ill in the Ohio \;ill('\-. tlicrc would 
seem til lie excellent ^rnund t'nr lielie\inii- that the eveles 
(•I the yield of the enips would How contiiuent ly with 
(he cycles ot' rainfall dui-iiifi; tlieif re-pei'i i\ c critical 
|ieiiod>. 



('l/cl(s in Ihc Ynli! ,,/ IIk h', pn .■<( malln Cnips ami llic 
('i>n-( spuniliNij ('iichs (if 1,'niiit'cll 

The method of hi-iniiinii the ''yclcs of rainfall for the 
critical period of growth of ti, • se\-ei'al cn-jis into rela- 
tion with the cycles of the re>pec'i\-e ci'ojis is -imilai' to 
the method that wa> emploxed in pa»inti- from the 
cycles of animal rainfall in the Ohio \alley to tlu> 
oorrespondiiifi cycle- in the state nf Illinois. The 
laborious i)ut diicct way of Ireatinji the proMem would 
l)c to conii)ute the periodouram of rainfall for the 
critical period nf iin,wth of each crop, and then to com- 
pare the residts with the corresponding periodo<ri-ams of 
Ihc respective crops. It may lie that this latiorious 
Mi'occss may excntually haxc to lie tolh.wed. Th(> 
process that has heeii a<loptcd in the pre.M'Ut investiga- 
tion makes several assumptions which it i> hifihly 
desirable to have clear in mind. It is as-umed 

(I) That the coui'-e of the aimual raiiitall is the mean 
course of the rainfall <if the part- of t!ie y(>ar 
and that. conse(iueiitl\-, hy coniputinu; the 
perioiidiirani of amiual ramfall, we obtain a 
>j:(>neral type <if curve loi docriliinji' not oi:lv 



luiiiifidl mid ll'i' ( '/■"/'N 



4.-) 



tli(> ;i!iiiu;il iiiiiifnll Imt al-o the niinfall <>!' 
any ciinsitlci-alilc part of tlic yrar. ( »r, iiiorc 
concictcly, that tlic amnial raiiilall and tlic 
raiiit'all of any (•(iii>i(icralilo liart of the yrav 
iiiav lie (lr<ciil)c(l l)y aii ('(luatioii of tin; foi'iii 






+ tti >ni 



\vlH>r(> tlic coii^taiits in tlH> scries may Ik- ditTcr- 
cut for the sc\cral jiarts of the ycai'. 

(2) 'I'liat whcn^ tlic con'cl;. ; ion lictwccn llic yield per 
acre of a iiartieular crop and tli(> rainfall of its 
critical season is liiy;li. the same p'tieral ty|)c 
of c((Uation will fit both gronps of data, the 
data of rainfall and th(> data of the yield per 
aci'i' <if the cro[)s. 

CV) 'I'hat hoti, "f the precedinfi, assumptions arc 
greatly fortiiicil if the compound curves de- 
duced fi-om tlic actual data of rainfall and 
yield >atisfy a i-casonahle tot of lit to the data. 

Tho Avorkins out of the conse.iuences of these as- 
sumptions is exhihiied in I'i^iircs 11, 12, \^, and the 
(■(Illations descri])tive of thi> several curves apjtcar on 
th(> correspondinjj; I'itiures. 

To mea>ure ihc^ dey;ree of fit of the curves to th(Mr 
n^spective data, we sludl emiiloy a (•o(>fiicient A', which 
may l)e descriiicd as the ratio of the arithmetical sum 
of the deviations of the oi>ser\ aiions from the curve 



m 



46 lCLi)in)inic Cycli.s: Their Lmr dud ('iiu.-^ 

Bushels of pofat-oes per acre 




+ 



+ 



— 

4: ^f ^^ 



+ 












:i ro 



■r ii f - + 



+ 






+ 



II 

31 



^..p. ^-^ y y ,„y^l,. ^, f / tj , . f fj 



litiinjdll (jftil ihv Cntps 

Tons cf hay pef^ ^cre 



47 




iunf^*/p^ 'jijd^'Li?jey^*S9Liyui ut liPJt.' 9u 



f 









O 



ri 

+ 



+ 



+ 






: _- + S 



5 T ^ 



b = N ,r; c 



- 


I'. 


I." 


I -J 


+ 


+ 


^ 


^^ ~^ 






CC 






cc 




? T 





x: 


.^ 


7 










^ 


* 


i- 


5 O 


+ 





1= '.-- 



I: T'. 



+ 



II 





i 


Wl 


^^^1 


11 






fl 


i 


. i^^^H 


i 


9 



48 



L\i>nntmf i'fjclis: Tlifir l.tnr cmj i'tmsc 



"u^he/s of corn per acr0 
J 5( 2 u 

-] — I — • — — — . — , — _ 







8 - 



" ' ,- 



+ 






■ = 'u : 



L + 



- N 



H fc re 






+ 



^- 



+ 



+ 



•/n>3"^ pue '■/nn'si^o^: ^i //e^wpu 



II 



f\iiiiif(ill mill III! ('nip 



49 



ili\ iilt'd l>y the ;irr;i iiiclinlcd lict wi'cii the cuiAC ami tlic 
>ti'aitilit line imlii'ai iiin the mcaii \aliic nt the (ili>ci-\ a- 

tinli-i. Ill till' ('HUalKill In tlir CnnipnUlKl cxclc i Ic^i'l'il t- 

iiiji the typical ciirNc with which we >liall ha\c t(i (leal, 
the first tci'lii nivcs the iiicaii \:ihic of the nli>cr\ at ic iii^^ 
ami the rciiiainiiiu; fuiir harimuiic tcnii^ tiacc the area 
ahniit tJK' lidfi/diital line (li-a\vii at a (h>taiice trom tlic 
hase line equal tn the mean \aliie ol' the (iKseiAalinns. 
'The reasdii tor adoptiiiii' lhi> comiilex coeliicient K is 
tliat the curves whose i-elati\(' dejfi'ees of tit are in 
([uestion apply to ([ualitatively different things. Ironi 
th<> nietlidd <pf calcidatin^ A', it follows that the smaller 
the \alue of /v. the belter is the dejiree of tit of the curv<' 
to the oiiser\ at ions. 

Passing now to the calculations referring to the 
represeii1ati\ I' ci'ops, we lind, 

I'or potatoes, the coi'iclat ion of the yield ])vv ac -e 
with the rainfall of its critical period .Inly and Au- 
}ji;ust is /• = .()(il'i. 'l"he measure of the fit of the coin- 
pouud cycK" of thirty-three years and eijiht year- with 
their setnilKirmonics is. in case of the yield per acre, 
K = I.!)7, and in case of the rainfall of the critical jieriod 
of growth, A' = l.;^(). 

For hay, the correlation of the yieM p(>r acre with 
the rainfall of its critical pei'iod March, .\])ril. May, 
June is r = AV2i). Tlu^ measure of the fit of the com- 
pound cy(de to the data is, in case of tlie yield |)er acre, 
A' - IJ)~, and in case of tlu^ rainfall of the critical season, 
K^lAV.i. 

For corn, the correlation of the yielil jicr acre with 






III 

'iff 



ill 



60 hciiiiiinnr Cj/'i^.s: I'liiir l.iiir <itiil Ciiiisc 

the r;iiiif;ill nt the crifical -raxin .Inly and .\M)Zii>t — 
i> r .."iS'.t, I'll,. iiira>iirc of ihc lit of th,. (■(iiii|>(Miii(i 
'•>''l'' '" 'Ih' <lala i<, Inr the yield per a( c. A' l.'iL', 
iiiid, t'nr the taiiil'all nt' the cniical season, K 1 .i'.O. 

I "'■ "■■il-. 'lie conipntalioii of the e(iualioii lias not 
Im'cii carried out lieeaii-e no critical jieriod of growth 
could l)e t'ound in which the correlation hetween yield 
and rainfall \\a.- hi^dier than r M. '{"he correlations 
were, for March, ;• .IM; f,,,- April, r- .147: for 
May, /• r_>(»: tor .lime, ;• :2\t7 : for July, r .140; for 
May, .lune, and .luly, r ._'!•(). 

Keferrinti now to the 1'itrMres II, TJ, \:\ and to the 
calculation- th.at have just heen reviewed, we observe 
that the coinpoinid cxcjes of yield per acre and of the 
rainfall of the critical seasons ilow almost c((ntrrueutly, 
and that the compound cycle of thirty-three years 
and ei^ht years with their semiharmonics fits the yield 
data nearly as well as it lits the rainfall data. 



('lirlis i)i th( Iitih.r i,f Cidii Fliichailidiis and In llir Cor- 
risptniiliiiii hi'li.r of M((ir /^fhrtiir h'dinfdll 

Does the cyclical movement of rainfall ii.'i\r a rhyth- 
mic movement to the tluctuatioiis in the yield of tlio 
(Toi)s taken all tofiether'.' The preceding section has 
treated the relation of the yield of tht> separate {Tops 
to the rainfall of their res|)ecti\(' critical seasons; \vp 
now ini[uire whether the yield of all of the crojjs tak(>n 
lotrether shows a tendency to conform to the cyclical 
mo\-ement of rainfall. In order to answer this ((uestion 
two [jrelimiiiary steps must lie taken: (I) A method 



h'liuijiill mill llir (iiijis 



51 



niiist he devised fnr iiu'asurinn the (luctii.'itinii in tlio 
viild iif the (Till )s when the c tups mic t.ikin ;ill tnnitlici-; 
:iiid I'J) ;i iiirtliud iiiii>t he d(■\i^(•d U<v ciiiiiliiiiini; the 
rainfall <i|' the cnlical in'iinds of the ^rnutli <>\ the 
;.<'\rial cioio. 'I'iii'X' tun stc|i> uc shall nn\v ((pn-iilcr. 
in regard to tlic first of tlior dri-idcrata, it is clear 
that the measure (if the llnctuat inii of crdps taken as a 
whiile slmuld lie liax'd upnM the lie-~t. inea-uic <if tlu! 
(lucluatidii (if the yield of the cnips taken siti^i^'. More- 
over, there is a general agreement, that the standard 
de\iati(iii of a ffeiiuency s(hein(' is a ^nod inea>ni(' of 
the seat ter of the oli>er\at ions nliout their mean \alne. 
A natural step, therefore, would lie to a>~unie that if 
the ol)ser\alions foi'tu a sei'ies in time, a jiood rela- 
tive measure of liieir fluctuations at dilierent e|)oc|is is 
alTorded liy the ratio of the (le\iations of the oliser\a- 
lions from their mean (li\ ided liy the standard (le\ ia- 
tion. I"or example, the mean yield of oats in Illinois, 
for the period 1S7(> to I'.HI), was '.U.l Im^iiels per acre, 
and the standard dexiation of the yield for the same 
peiiod of time was cr ,").-J husheis. The \ ieid per acre 
for the year H»lt) was ;5S.() liushels. If A lie taken to rep- 
resent the deviation of the yield of any year from the 
mean yield of the whole period, then the A for l!ll() was 
;is.(i lil.-l =li.r), a! 1 the fluctuation for I'.HO was 

... ^ 1.27. Similarh-, for tiie xc.ar I'JOS, when the 



<T .')•. 



yield was 'J.'M) liushels, the fluctuation wa 



l.t) 



It hapiiens that in the case of oats, there is no secular 
trend to the yield, hut when the secular tread exists, 



52 Kcanoiuiv Cifchs: Their l.mr nial Cm.^i 



i' liiil~I lie rllliilli;iti'(l IicImic the tl Ijcl ll:i t h i|| i^ ciiin- 
pllli'il, 

III 'l':iiili' III "I ihc \li|irliiil\ 1.1 till- c'KiliIrr tin- 

tlllil ll.il |(.|i |(i|- t :irli (.1 llii' |(ir!> -iilir \i',ii-, |s7l) l!)|ll 

I- tiivcn tnr ciini, ii:ii--. Imy, and imlaiiM'-, |',y l;ikiiii; 
the aluci.iiic -iiiii (iT the (linl iiati.iii- Inr all ll.i' ri(ip> 
lni' aii\ \i^\\^\\ \ ( ar aiid du nliim \<\ i'. mr ihr nuniiicr- uf 
'111' VV\>]\^ a liira-IIlr lit' llir llllrl i|a I H i 1 iif llir iTii|i- 
t.ikrii nil tnuflhif i^ iililaiiiiil. 'Ilii^ tiii'.i urr \\r ~!iall 
ii'lcr III a^ till' iiiilr\ 111' till' lliii'i iiai mil ul rmp-. Viir 
iiiilr\ lur rarh 111' ihr >i'ar- lN7n I '.Mil i~ irciinlcd m ilir 

l;i-I riillllllll n| Talilr III. 

I III' imlcx 111 rin|) lliirtiiatiiiii rninpiili'd in ihc maii- 
ni'l" tlial li;i- jii~l lirm dr-ci ilinj i^ iri;ardrd ;i-> ;t iimrr 
;iri-iiral(' iiira-iiii' dl' the tiiiri ii;it lun <i|' ci-up^ than 
wiiiild lie (liilaiiicil tnnii all iiulfX tniinrd l'\' lakiiii:- a> 
thr lliii-tiiat imi fur carli year, in ra-r <il' carli cmp. llir 
ratio (if till' di'\iatiiiii finm the mraii di\idril liv llir 
liicaii. If till' iTiip-^ ditfi'T ill ihcif rdcllirii'iit-i nf \ana- 
titiii. that i ■ In >ay, if thr i'atin wIhtc .1/ I- the iiiraii 

yii'ld and (r i> thr -taiidard dr\ iat imi, i-^ iint the ^alil•« 
l"i' all ( I :w, llifii thr crnp with till' lar;ir-t ciu'lhcinil nf 
\ a fiat imi wniild ivn ivc thr lartir-t \\rit!:ht it, t hr jimrfal 
iiidrx. Thr ciirlliriciils <if \ariatinii I'm' thr cr.ip^ in 



111' 'ralijr : rr, ii>v cdi-ii, 



.SI 



. I ■)/ ; II If piitali II 



. L'i7 : fur (lai-. 



111- I ■1'^ ■'■) ■'") 

■ I'll : tnr hav . lo7: llir i)iit;iiii(-. "' "' 

7().-,| 



ol.tl 

- .X'A). If 

llir ii~iial iiirthnil of fiirmiiiir imlcx nuiiihrfs wrt-r ciii- 
liliiyrd ill liii.s cax' to inca-urr crni) lliirtualiim.s, tlie 



luiiiijiill mill llii f '/'((yy.s 



aJi 



wvcrnl cvit])^ wniiM, in (■(in~i'(iui'iiii' dI' llicir ililL rent 
\';iri;iliilil ii-, iccci\r (Ii~|iiit|)(i|| iniKiic untilii-.. I In' 

IIK'IIi'hI nf r.ilrllhilllii; the llii|r\ wliirll We li:t\(' Clll- 
|>|nyi(| (ili\ i.ilf^ 1 lii^ (lilllclllt \ . 

Il;i\iiin iiiiw iiliiaiiicd ;iii indrx dl the lIuchiMt ion d*" 
criip--. We lir\l cuii-idcr t III' iiicl li<i(| n|' ciiiiiliiiiiiiji; t 111' rnill- 
lall of (lie clil ii-;il pri lull- dl' y;i(i\\ I h fur llif >c\cr;il crnps. 
'I lir ini'lhiiil will lie clr;!!' ll Ur ln'lll' III niillil lli;il lln' 

(■lit i I'M I peril II I III' nii>\\ til III' a I'll ip i- till' <■ unliiiiat imi i)f 
iii(iiilli> wlio-f rain!. 11 u;i\i'> llic liiiilii'-l cm rrlat imi with 
till' yirlil. Thr im-aii ('I'lrrtixr iiiiiiitlily raiiilall lur tin- 
• ■fit iral in'iiml III a ciMp i- till' 1 1 it a I raiiilall ul tin' ni lira 1 
pi'iind 111' Sill iw III di\ idi'd liy I lir iiiiiiil'.'r i>t timnl li- iiiak- 
in^ up llic rii'iral prfii'd. Ill I'a-c nf lia\', I'm' cxaiiiitli', 
llic criliral jirriud nf ^imwlli is Marrli. April, May, 
.luiic. Till 111! 11 crfiTlixc rainfall fur ;.ii> )ii\iii year 
wmild 111' till' total rainf'll fnr tin' fmir iiiniilli-. March. 
April, .Ma> , .luiii'. dixidcd liy the niiiiiln'r uf ihr iiiiii.tlis. 
If till' mean ctfcciiNc innnllily riiinfall fnr tlic >('\c- I 
crn|is i> siiinnicd fnr each year and di\ ided 'ly the nuiii- 
lier nf crops, a measure i- nlitaiiied nf the mean effect i\(> 
iiinathly rainfall fnr the crniis taken all tn^ether. in 
Tahlc i\' nf the Ap|)eiidi\ to thi- chaiiti r the mean 
erfecti\e rainfall of the sexeral crop-, and of the crops 
taken all tntiether, i- taliulati'd I'nr eiich of the years 
ls7(l I'.tld. 

We h;i\(' iin\s an index of the iluctiiation of crops and 
an index of the iiie;in et'fecti\c rainfall of the critical 
periods of the ci'iijis. The correlation hetweeii tho 
two serit's is r = ..")S1. In 1'ij.nire 14 are traced the ^rajihs 



Ih 



r>4 



Ki'otnifnic r//i7fN; Their Iau: and ('<iu,se 



Inde* cf fL>ctua*''on of crops 




/ft\^u'P~i A'fi^^uOi.u ^/i//JJ^J ue<i^y 



RuinfiiU iiud lli( Crop.- 



55 



m 






of tlio r'onipoiiud cycles that dcscriho the two scries, 
each fii-apli consist iiifi of two cycles ami their seini- 
hannoiiics. a tliirty-three years cycle (lescrii>iii^: tlie 
liroiirul-swell and tlie smaller cycle of ei^ht years siiin- 
inarizin^ the minor cyclical movements. The measure 
of the defiree of tit to the oi)servations is, in case of the 
yi<'ld ciirve, iv =2.4t). and in case of tlie rainfall curve, 
A' = 1.»)S. Tlh yield cin-ve reproduces the general 
cliaract(>ristic features of the rainfall curve. 

Our iiudiut^s with reference to lh(> cro])s tak(>n to- 
gether are similar to what we discovered in case of the 
sinfj;le crojjs: The yield p( r acre and the rainfall of the 
critical season are liighly correlat(>d; the rhythmical 
n. ements of the yield and of the ("ffective rainfall 
may h" accurately described hy a comi)ouud cycle of 
thirty-thre(> years and eight years with their semi- 
harmonics; and the yield curve reprotluces the general 
cluiractoristics of the curve of effective rainfall. 

Passing now to a summary of the contents of this 
chapter, we may collect our results in a series of prop- 
ositions. 

(T) The yield per acre of the four rejjre.sentative 
crops, corn, hay, oats, and potatoes is associ- 
ated with the amount of the rainfall of their 
respective critical periods of growth. In 
three out of the four ci-^es the degree of cor- 
relation lies hetwe(>n r -= .580 and r = .(itiO. 
(2) The rhythmical changes in the yield jkt acre of 
the cro])s and in thi rainfall of the resi)ective 



' '1 






56 



Enuitiniir Ci/clcs: Their Ijv.r ami Cause 



critical seasons may lidtli Ix' accurately de- 
scrilted i)y a cmnpouiid cycle cnniposed of a 
thirty-three years cycle with it< seiiiihar- 
iiioiiic, which siiiimiarizes the ^iduiid-swell of 
the moveiiieut . and a MiixM-jxised cycle of ei^iht 
yea'-s with its seiniliariiioiiic, describing t'.e 
shorter rhythmical movements. 
(3i In three of ihe four re])resentative crops, tlie 
comiioimil cyi'les summarizing th(> changes in 
the rainfall of the critical jx-riods of growth 
and the chaiifies in th(> yield i)er acre of the 
crops are so nearly congruent that, consider- 
ing; the high correlation of the yield with the 
rainfall, one may conclude, with a higli degree 
of pnil)al)ility. that the rhythmical movement 
in the weather conditions represented by 
raiid'all is the cause <-'' the cycles of the crops. 
(4) The index of the lluctuation of the crops taken 
together, and th(> inde>: representative of tlu; 
mean effective rainfall during the critical 
seasons are highly correlated, r = .")84. 
(o) The rhythmical changes in the index of the 
fluctuation of tlu^ crops and in the index of 
the mean effective rainfall are accurately 
described l)y a compoiuid cycle which is made 
up of a thirty-thre(> years cycle and an eight 
years cycle with their scMniharmonics, and 
these two compound ciu-ves ar<'. in their gen- 
eral characteristics, much alike. 
(G) The invi-stigatiou of tlie crops taken singly and 



h'dint'illl (dill thi Cra/ls 



57 



taken tojicthcr leads to the fieiierai coiiclii- 

sidiis: 

((/) that there is a rliytliiiiical iiiuveiiieiit 
in Ixitli the yield of the crops and in the 
rainfall of the critical periods which is 
>uniniarizcd in a compound cycle, in 
wiiich the constituent elements are a 
p-ound-swell of thiity-thre(> years and 
its semiharmonic. and a shorter super- 
posed cycle of v'lghX years with its 
semiharmonic; 
[h] that tlie cyclical movement in the 
weather conditions repres(>ntod by rain- 
fall is the fundamental, persistent cause 
of tlH> cycles of tl;e crops. 



m 






111 



m 



AJ'PKNDIX 



TAlU.i: 1. TUK (Ki'l'S I IK Il.l.lVnl- 



YlH.H I'FR .\rnr. OF 

(liii-.. IS Hi -111 1 -■ 



YlKIl) I'FK A< KKOr 



^ KAIt 



1 


A' IIM, 1 


|{> iM rui> 


1 


vu.i. ! 


> IKLl> 


1S70 


35.2 


35.2 


1.S7I 


38 3 


38.1 


ls7J 


39 8 


;('.» 4 


is7:{ ! 


•Jl 1) 


20 4 


Is7l 


Is (1 


17 2 


is7r) I 


;ii :; 


33 3 


|s7i) 


2."> 11 


23 8 


ls77 


2'.i n 


.'7 I'l 


ls7S 


27 1 


■J.I .1 


l.s7'J 


3."i 1 


33 2 


1^S() 


27 . ■_' 


2.-| 2 


ISSl 


19 1 


17 2 


ISS2 


23 11 


2(1 t) 


iss:j 


2.1 () 


22.1 


ISS4 


30 


27 1 


1S.S.-) 


31 t 


2s 3 


iKSti 


21 :. 


21 2 


1,SS7 


19 2 


1.". 7 


188S 


3.-. 7 


32 


1X80 


32 3 


2S 1 


1K90 


2(i 2 


22 1 


i8«n 


33 .-. 


29.2 


1892 


20.2 


21 7 


18<,I3 


2-). 7 


21 () 


1S94 


28.8 


23.9 


1805 


37.4 


32 3 


18!tt) 


40. 1 


3.T 2 


1S<»7 


32 .') 


27 


1898 


30 () 


! 24,3 


1890 


3().0 


1 30.1 


190<) 


37 () 


30 9 


>1M)1 


21 1 


l.-| 1 


l'.H)2 


3s 7 


3-j 2 


19();{ 


...> .) 


2.') ."> 


19(H 


3t) '> 


29, ti 

( 


19lt.-. 


:f9 . s 


1 32.7 


I'.KHi 


:;■, 1 


2s s 


l't07 


3(i 


2s 1 


I'.iOS 


31 11 


2:( 8 


1909 


;;.■> 9 


27 't 


1911) 


39 1 


3(1 '.1 



Yin.D Tkii 

Ai IIK IIK VlHl> I'KH 

Mm. i.s I .\riit; OK I 

i .iN» I t)^T^^, IN 

AiTiM. I lin.i.uu |Tou*200(l' HrsuEUi 



81 

(i! 

( .1 
40 

:>.■> 

12S 
7.'i 
9:'. 
1 17 

8S 

7."i 
4^' 

S."i 

92 

79 

tl7 
33 
so 
99 
30 

12 

-",.> 

.■)3 
.■|0 
77 
97 
3S 
70 
9t( 
90 
3.") 
US 
72 
lOs 
7."i 
97 
s7 
71 
91 
7.') 



M (1 


1 Is , 


2i. (1 


(1(1 s 


1 .11 ' 


3:1 1 


71 .'i 


1 3.-. 


;'i(i (i 


:i9 3 


1 2."i 


30 


.Ml 


1 20 i 


17 .") 


12(1 s ; 


1 37 i 


■a:\ 


73 (1 


1 10 


20 


'.(1 4 ' 


1 (10 


:!7 


ii.-i 1 1 


1 19 


:i,"i '.» 


s.'i 9 


1 21 


:i2 


72 7 ' 


1 l.-> 


31 8 


4,-| 1 


1 3(1 


33 1 


81 S 


12.'. 


40 7 


89 


1 I.-, 


3(1 1 


7.'i 7 


1 1(1 


:!.' s 


s;i ,-, 


1 30 , 


32 8 


(l:i 3 


1.31 ; 


31 S 


29 (1 


sO 


2!l .') 


7.'i s 


' 40 


3.'. s 


'.M (1 


1 39 


37 ."> 


2."i 3 


1 30 


21 


s7 1 


1.25 


31 


Itl 9 


1.25 


2(1 3 


47 (• 


1 21 


• )- ■) 


lit 


1 U 


3(1 1 


71 2 


.(1(1 


21 I 


9(1 ',1 


1 3S 


2s 


31 7 


1 29 


32 


(13 .") 


]..')( i 


29 


89 2 


1.29 


38,0 


83 


1 27 


38 


27 s 


Ids 


2 s 2 


110 .'. 


i.-.o 

1 ". 1 


37 7 


(M -S 

!(1(1 1 


1 .It 

1 :((. 


:;2 


111! s 


1 3.-i 


3.'i . .'1 


ss ll 


.9s 


29 .■> 


78 4 


1.10 


21 .'> 


('.2 2 


1 .-,3 


2;f 


81 9 


1 l.'i 


1 :;(i (1 


(l.'i 7 


1 :i3 


j :is 



.)8 



RaiiiJaU and the (.'rojix 



50 



TAlil,i: II Ml.\N MiiMlU.V 1{\1M\I.I. 1^ ll.l.IN"! 



Yeah 



MARfH 1 Ann 



MkAN MoNTHl.r IlAINfAII. 

•IrVK 



May 



1S70 


:i '."2 


1 ):> 


1S71 


3 :!i 


2 17 


1S72 


2. -.9 


3.39 


lsr:{ 


1 7.") 


4 9S 


1n71 


2.:i9 


3 50 


is7r) 


2.s:5 


2 no 


|N7t) 


5 1:? 


3 . 3S 


ls77 


4 ()2 : 


3 53 


1n78 


:j 1)4 1 


4 . till 


1S79 


2.59 1 


2.42 


isso 


:?.:n 1 


4.29 


issi 


:Mf. 1 


2 IS 


1SS2 


4,00 1 


4 (M) 


l.vvi 


l.Sl 


4 10 


1.SS4 


:i ;ii 


3.3(1 


LSS,-) 


().■):{ 


4 13 


1SM> 


:5 02 


3 (10 


1SS7 


2 :!7 


2 4(1 


1SS8 


4 09 


1 91 


ISSi) 


1 <12 


2 00 


1S9() 


4 :\\ 


3 75 


l.V.II 


;i 4:5 


2 91 


is', (2 


2 17 


(1 43 


is9:i 


3.:n 


7 (14 


1S94 


2 9S 


2 73 


1S95 


1 72 


2 17 


IV Ml 


1 91) 


2 SI 


ls'.i7 


1 tl 22 


4 53 


1S9S 


1 7.70 


3 17 


IS'. 19 


1 :J.19 


1 (14 


19(H) 


2 12 


; 1(14 


19!)1 


3. so 


1 S4 


19(»2 


3.04 


2 55 


191 »:{ 


3.23 


4 51 


19,tl 


(i . 4 1 


3 7)1 


I9(i:. 


2 32 


:i ss 


I'.KMl 


4 0'.) 


2 ()'.) 


19(»7 


3 -r. 


2 SI) 


I'.MIS 


3 21 


1 5',) 


I'.KK) 


2 112 


5 9t 


1919 


:',2 


3 . (Ki 



\ 


('>4 


3 


(M) 


3 


(10 


4 


s7 


•> 


25 


1 4 


57 



4 (IS 

3 13 

5 01 
2 10 
5 '.)3 

2 2(1 

(1 no 

5 3S 

4 10 

3 (13 

4 07 
2.90 

5 IS 
5 11 
3 S(i 
2 19 



S (H) 

4 24 

3 2'.) 

2 34 

(1 0".) 

1 'l 

() 2(1 

(1 41 



1 93 

4 00 

5 (IS 
2.1s 

3 . 45 
5 . 30 
5 . 53 
7.39 

2 72 
4 33 

3 53 
5.93 
11 (11 
5.51 
5.13 
5 . (13 

4 42 
1 94 

4 . SO 



35 
5S 
11 



n 

2 . (is 
4.14 

4 2S 
4 71 
3 (H) 



4 51 1 


4 31 


1 S(i 


3 55 


3 7S 


7 . 77 


3 25 


3.03 ' 


3 29 


3 2s 1 


1 27 


3 (19 1 


2 39 


3.0s 


3.95 


4 17 1 


S 07 


3 14 1 


4.23 


4 01 


5,04 


2.. 12 j 



1 




Septkm- 


Jil.v 1 


.\t tir^r 


BF.R 


2 S.5 


3 <.)5 


3 09 


3 11 


3 50 


1 22 


5 00 i 


3 05 


4 29 


3 9',) 


1 77 


3 19 


2 (Hi 


4 2s 


3 95 


9 37 j 


1 90 


4 00 


1 91 


3 S3 


4 33 


3 27 


2 7 s 


2 29 


3 S3 


1 U) 


1 (11 


3 41 


4 Si) 


1 .4S 


3 10 


3 (15 


3.59 


2 5S 


St 


4 04 


3 10 


4 05 


2 OH 


4 SO 


1 SO 


SH 


4 09 


2 40 


4 . SO 


2 SO 


5, (HI 


5.07 


1 15 


3. Ml 


4 SI 


2 to 


2 40 


3 25 


S3 


4 31 


1 to 


4 45 


1 22 


3 7S 


203 


2.9(1 


3 04 


1 ss 


4 71 


1 02 


3 71 


3 03 


2 01 


2 20 


'.10 


3 (19 


1 5S 


1.74 


4 53 


01 


2.70 


3 00 


17 


2 95 


5 79 


3 5',) 


1 1.19 


99 


2 S4 


4.70 


5.07 


3 12 


2.70 


2 23 


1 15 


' 3 72 


3 59 


J (13 


i 1 9! 


1 '.)7 



tl 

23 
7s 

5S 
39 
32 
')0 



( <1' 
I .".' 
1 2. 
3 
I 



41 
15 
5)1 

3') 
12 
51 



24 
s5 
43 
S9 
15 
3S 
tl 
25 



4 0; 



60 



/■; 



•ADUDiniC 



Cjicli.s: Thiir Linr uml Caii.^ 



'I'.MU.i: 111 In:>i.\ "I 
1 ;.i\ ! i!i>M •nir. Mi; \n 
l!i.i\ii\ Mill, "■ 



'i.i I'l r \ I iii\ UK l'niii'~ -^ " l)i;vi\- 
\iii;ii III)-; Si:( I i.vit Timmi ii \> iikkn 
Sr\M)\K]) |ir\i\iiii\ 



il 




1 






1 


1 


1 Index 


Cnnv <>M- ' 


IK, ',' V SrMoK ' 


.S|\f UK 


1 or 


Y ». Ml 


^ .i 


^ '"'^ I'.,^,-,m: 
1 -^ InrrrA- 


<),'i\n\ K 

•'l.irTI \ 


KMB I VTIIIS 




J »J 


<^ « I TIDNS 1 


TIONS 1 


1 ^"'■' 


; 


1 
1 




1 




i Chop* 


IS70 


1.43—1 01 


"*> 


.1.- 1 ss 


1 71) 


+ .l2i+ .o:i 


1.S71 


1,!»U| .:::i 

■2 \l\ 1 (M> 


,00 


— 12 2 20 


12 


+ 1.S4! + .40 


1,S72 


.>.) 


,17| H,.'..'. 


,01) 


4-:{ .-)5 4- .SO 


is7;{ 


1 ij JtI - .:i:'.' -1 -it; '"' 


:i,(H) 


-:{ (HI - .70 


1S74 


1 (17 --_' I',;! - .111 - 7o' 00 


."1 11. ■) 


.-, ll.-, -1 11 


l,s7-> 


1 10 :il :i:i 


2. 12 4 10 


,00 


t I 10 rl 01 


ls7() 


- ,f,7 "2 l'.> r.i) 


i:;; 0:! 


2 SI) 


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,00 ;{ 71 


.00 


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.47 


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(ill 1 s7 


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' 













Hilinfdll (lliil III' Ci-'ips 



61 



\r.i 



Vt^ii 



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l>7l 

1n7-' 
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l-vTl 
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is7r, 
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1SS2 

iss:! 

I vs.-, 
issl 

^s7 

isss 

lNS',1 

IVM 

is'.t:! 

IMC, 
IV hi 

l.s'.)7 

IS'.tS 
IV.Mt 
1900 
I'tOl 
1'.) L' 
19();{ 
I'.IOt 
190.", 



1\ 



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1 71 

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a. 01 



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iAl 



CIIAI'Ti:!? IV 

Tin: LAW oi I)i;m\M) 

Kmihi mail ii'ulit die Nadifrau'it'iiiiktidii uciiaiicr fi-l.-tt'llt!i. mi 
griiail. ila-> u ir liiclit l.l(.>s rili cilKlriitif;!'.-. >(ili(liili Mti kclikrclis 
Hoiilla) tii'uiiiiKir.' Ic!i ^laulic dir Aiitwurl /u ii'M: W i Idi' 
(•in [iliaiitasti.-rlii-. Inlcifaiiiicii-riilirii rliriiliaiki it ilir -.v irl>(liafl- 
lii'lii'ii Noruaiiyc >t(t(r \\Ccli>cl i -. w' 

.ln>KI'M Snil MI'Kllli. 

(^iKsiiiiNs MtTcrliiit!; for tl.c Ill(•^t i);irt tlic sujiply of 
coinniuditics li;i\(' thus far liccii the olijcct (if oiii" iii- 
\('stiiiati(in. liiit tlic iii(|uiry as to the cause and law of 
('('oniiiiiic cycles must extend to a consideration of 
cycles of \alues and prices. Since the rhythmical 
\'arialion in the >upp]\' of crops pi'oduces its etTect upon 
cro]) ])rices in accordance with the laws of demand for 
the several ci'ops, the ol)\ious liist and necessary step 
in iiriiminji the I'csults of tlie precedinji chapters to iiear 
upon the ([notion of the cau>e and law of economic 
cycles is to >ol\(' the problem of the relation hetween 
the \arialion> in the sii|)])ly of the several crops and 
the resulting \ariations in their respective prices. It 
is rcMiuircd to derixc Ifom existing data the concret(> 
laws of demand for the representative crops. 

77.( Thiarij (tf l)( nnniil 

The mathematical treatment of the theory of demand 
furnishe> two doctrines 'lat are of im])ortaiic(> in our 

02 



l[t\ 



Till l.iiir llf l)l ; 



</ 



(i:{ 




MM X 

I'"l(iIUK ITi. TllC 1:IW cif ilMIKltlll. 



suli>c(|uciit work : 'I'lif (Idctriiic of the unifdriiiity nf the 
(IciiKiiul function and the ddctrinc of tlic cla-ticity of 
(Icinand. The exposition of tlicse two (lo(■lI■ine■^ will lie 
facilitatecl liy reference to I'ifiure 1"), in uliich, accord- 
inn to the u-ual ■.naciice, (iuantitie> of commodity are 
measured upon the axis 
of abscissas, and the cor- 
respondiiip prices per 
unit, upon the axis of 
oi'dinates. 

The doctrine of the 
uniformity of the demand 
function, which is trace- 
ai)l' to ( 'ournot,' hut is 
os])ecially stressed hy 
Professor Marshall, has l)e(Mi jiut in these words: 
''There is then one general Imr of ilimaiiil viz., that 
the greater the amount to lie sold, the -mailer will 
he the price at which it will lind i)uicluiseis; or, in other 
Words, that the amount demanded increases with a 
fall in price and diminishes with a rise in j)rice." He- 

' (''UiriKit; /i'((7(( 7(7/(.< sur lis priiirijns niiilliiiiialiijiiis lU hi lliinric 
(/(>■ ;'/c-/)(xx(N, §§-'1, -'2. Assuming tlial tlic rclatiuii lictwccn price 
and tlic .ainounl dciiiandcd is rcprc^ciiti'd hy Fip), he says, ji. .■)4: 
''Si la fiinclii)ii I''(i>,) ot coiitinui', clic jouiia dc la jiroprii'tr'' (■(ininiunp 
a tdutcs li's fdiictiiiiis dc ccttt' iialurc, ct siir la()U('ll(' rcposcnl laiit 
d'applicatioiis imiMii-lantcs dc 'I'analy.sc icallicii aticnic: Ics varia- 
tions dc la dcinandc scmnt sriisihlcnicnt proiHiilioncllcs aux varia- 
lions (hi prix, lant (luc ccllcs-ci scriiiil dc pctitcs fractions du jirix 
orifjinairc. Uaillcuis, ccs variations scront de sifincs contrairrs, 
c'cst-iVdirc (ju'il unc avifinicntatioii dc prix corrcspondra unc dimi- 
nution dc la (Uinaiidc." 



II 



M i:>- 



iiiiinif I 7 



( lit li v.' Till If l.iiir mill ( niisi- 



fcrriii^ Im liuiiiv l."(, till- -i.-ilfiiiciil iiiraii> tli.ii il' .-it 

illl\' linilit ill the (IcIm.IIhI CUIAC />/>', ^.•|y the pniiil /', 
a >tf;ii!ilit line is (liauii l;iM^:riit to the iiii\c, tin ii iIim 
trmuiiniiictiic t:iiiy:ciit of t hi' aiii:lc w hidi the hi i' ii akcs 
with the pti-it i\ (' direct i 111 dt' the a \i- (if ./', is iir^ati\c. 
Ill l'infe-.-(.|- .Mar-hall's \\erl-: "riii < .n- uiiivcrsji 
rule to which the (Iciiiaiid cuiac coiitoinis is fliat it is 
iiicliiK (I negatively thfoutihoiit the whole ei' it > Iciinlh."' 
As we |irocee(| we shall find that the law orde'Maiid for 
.some coiiiiiiodities does indeed coiit'orin to t e type of 
ciii\ e w liicli has jii>t l)een de^crilied. Imt it will he a pa it 
of the Work of the next chapter to ow that the doc- 
trine of the iiiiii'oriiiity of the demand ■ inction i- an 
idol of the static state of the iiicthi I of ca'T/s 
ixirihns which has stood in the way of tiie succcsm'uI 
treatment of concrete dynamic pioMems. 



\ssiiiiiiMti that the law of demand for fi pi\'(Mi com- 
modity is re|)reseiited hv the dcscendiufi; curve DD' in 
Figure I-"), the elasticity of (lem;iiid for the i iininodily 
when (1)1 units are lioujiht is measured hy the ratio 

WW (jr .,., , .. , . 

() 1/ ^ I' \l' '"^ '" ^''■^'' '" ti'''"''''*' 'I'll ■^, li the price 

of the comiiKidity undergoes a small chan^ie, theamount 
ol the commodity that is demanded hkew'is(> undcM'fioes 
a -mail chantie. and I'le decree of the elasMcity of de- 
mand tor the commodity, in the gi\cn state of the mar- 
ket, is mea>iired hy the ratio of the relati change in 

' .M:i;>l :i!!; I'ni^rijili ■< i-J Eciiii<>niir<. 1th <<lit,, |>i.. i71, 17! r.i.lc _'. 
Ill till' -ulir.r(|ili lit rra-iiliin;; Wi- ,-1 all Call tlis t} | c ef ill :; and 
I'Ui'vu llic ni'',alivc t\|)c. 



Till l.dir III hi 'iiiiil 



05 



Ih,. lUiM'ilIiI .1. !n:iliclci! In thr n.'ill nl:i1i\. cli.-iiilir HI 
thr pri.r. Or, iimiT .lcriiiit( 1\ . il a tall 'I 1 |" i' •'rut. 
in pnic wiuilil ..iii-c ail ini'n r d' '_' ]' f i-''iit. in inr 
,^,l„„,Iit .Irliiall.l. .1 thr cla-ticity <>l ^IrlhMInl V,-iil,l li.' 
tun. ' II ■■•A iill "f 1 pri' ..•Ul. ill priir W(Mllil call-c all 

incroaso of '3 [kt I'l-nt. m lli'' anii'Hiit (IcihhkI'iI, tlic 

elasticity nf (Iciiiaiul unuld !"■ niic-tliinl; and -^n .,n." ' 

it will l.c nliMT, .■,[ t .at Ml.' Ihrorv nf cla-tirily of 

([.•niaiid in tins (■la--ica! tnrni i> pn-mt.-d \- 'he 

point of vii'W of inlinitiMinal cliaiiy.*'- m tl"' '\^'> '-"i" 
rial)]('s . iiiiii' and roi niodily dciiiandcii. ll p,i\i'S 
the <lctircc of v\. licily of dcniaml for a |Miiiit in Iinic, 
for a ^ivcn >tal. of llif iiiari.rt a>-uiniiii; all otl.cr 
tliiii(is to rcn.ain tlif saiiii'; and for llii> iva-'ii it may Ix' 
said to Mvat of ,la-tirity of d. ;iiand from a Matical 
p,,iiit nf .'w. But ll' > i- not It-; mo>t >■ riou- limitation. 
It p.-tulatc- ,1 kiowicdtio of the demand lurv.- ami 
V hil' it ni\c> an e\po-itio' of the metl -m hy u •iich liic 
deniv. o' ela-ticity of doiiiaiid miy;hi he del.rmined 
provided ihr dem.aiid curve were kiKiwn. there have 
lieen ^rave doul.ts a> to whether 'Ik- i)ractical (lit! ult\ 
of (leiivin<!; the demaii'' curve wo .Id ever he overcome. 



HI 

1; 



The iH-ohlem hefore us '.^ to derive the demand curve 
from statistics; to moasiuc the det^rce in which it is an 
accurate d'scrijition of tlu' change- of actual industry; 
and to fiive the numerical coetlicients • ' ela-ticity of 
de Kind for lyjiical commodities. 



Marshall; I'lmripli s of Erunomlrs, Itli edit., ;.P. 177-178, 



note. 



Pi 

191 



66 Eiiiintifiu- (i/ili.t: Their Luir iiml ('(iu> 



Slillistiiill I. nils III' l)(iniiiiil 

'l\Mi t'limlaiin'iital (Ict'cci- in tlic ciiiirnl ilicdi'cl ical 
iiii-iIkkI (pf tical inn rcniMitiiic ((iir-l mn-- aiT rxnnplilicd 
in the case nf the tliinrv i>t' (iiniaii(i: lir-l. llic a-^uiiip- 
t ion i^ niaijc that nil ulhir tlmuis lunni iijiinl itiic nid 
cwlins pnriliiis . an incrrax' in the -u|»iily nf tlic cdtn- 
liidility will lead to a (•(.iic-pDndiiiK tall in 'ln' price: 
M'i'dndly, il i^ a>-inni'd thai tlir ciincfcli' pruiilcin (if 
tlir rrlaliiin of prirc and "Uppl\' nf coniinndiiy will lie 
sinipliiird liy allarkin^ tir-t tlir cnn-l iliicnt ricincnts 
(if the (|U('^iiiin latiicr than liy atlackin^i directly the 
prdlileni in il~ full ciinci'eteness. Neither a.-~unii)tiiiii 
is sat isfaclcry imr indeed adnii--ilile. Ihe ''other 
tliin^;s" that arc Mipjxi-ed to remain e(iiial are seldom 
mentioned and are ne\i'r complelelN' enumerated; and 
(•(in>e(iuenlly the as>um|)tion that, other unmenti(>nc(l 
and un(nuinei'at((l factor^ remainini;; c(in>tant, the law 
of demand will he of a ceilain type, i^ reall\' lantamoimt 
to sa>in^ that iindei' conditions which ai'e \inanal\zed 
and unknown, the law of demand will take the .-upposed 
delinite form. The liurdcn of proof is upon anyone 
usiny; this method to >hiiw that the ;i>>umpl ion does not 
at least in\(il\('a ph.\>ical inijiosvihility. 

The second of the aliox'e two as>um])tions is not more 
satisfactory than the first. It i-cpi-oduces the defects 
of the first assumption with others superadded. The 
movement of prices results from ch.ansres in many 
factors: .\cc0rdinj2; to the statical method, the method 
of caliris pdrlbns, the pr(i])er course to follow in the 



Till I. (Ill- of l)< iniiml 



vr 



(•\pl;iii;iti(iii (if the pliciiiiiiicii'iii i- to iii\ r<t i^atc in 
turn, tlic<iic!ii;ill\ . ihr ttirrt npnii |iiicf (if <;i<'h taclcir, 
(•(vlins iinnliiis. anil then linally to makf a -yiitln'sis! 
I'.iil if Hi caM' uf the iclathiii of laih factor I" pii'-c the 
as-ninpliiiii ((ill I IS iiiiriliiis in\i>l\t- lar^i' ami at lca>t 

(lUi'-Il'ilialilf ll\ putlic-c- <liifS (lUf Hilt cuiiiplclrly Id^C 

liirnxlf in a maze <'f iiiil'lnit liypntlioo wlicii he >praks 
(.f a liiial >yiilli(-i- nf tlic -cvctal fnrcl>' \\C ^llall not 
adoiit thi> lii'wildciinti Uicthod. Kut >liall folluw the 
i)ppu>itc cduix' and attack tin pidlilcni of the irlation 
of prices and >u|)ply in it- full concictcncss. 

riir fruitfulnc» of the statistical tlicory of correlation 
stands in siiiuili^ant conliasi to tiic \ast liarrenn(-> of 
the iiietliod tiiat has ju-t heen de-critied, and tiie two 
jnethods follow oi)i)ose<l cour-e- in dealing with a 
problem of multiple effects. Take, for example, the 
(juestion of the effects of weathei' upon ciojis. W hat a 
u.seless hit of speculation it woidd lie to try to solve, in a 
hypothetical way. the (jUi-tion as to the effect ol rain- 
fall upon the crops, other unenumerated elements of 
weather remaining; constant'.' The ([uestion as to the 
otTect of temperature, nrtirls ixinlms.' How, linally, 
would a synthesis he made of the sev(>ral indi\ idual 
effects'.' The statistical method of nniltiple correlation 
formulates no such vain (lueslions. it inijuires, di- 
rectly, what is the relation hetween crop and rainfall, 
not calcris piirihiis. hut other things chanjiins accord- 
ing to their natural order; what is the relation hotwoen 
crop and temiK-raturc, other thinfrs eonforminp; to iho 
oliserved chanpc-s in temi)erature; and. 'Inally, what is 



68 hiiiiiiiniif ('ijcUs: Till ir Lmr mid Cititsc 

the rclatimi lictuci'ii cnii) ;iu(l rainfall for cinislant 
vair., s lit' irriipcratiiiv? '["he pniiilnu (if the ct'fccts (if 
the (■(iii>litu('iit fncldi's is xilvcd (inly aftci' the iiuiro 
Hthcial |ii(ililciii lia> rccci\('(i it> --(ilutidri. 'I'his iiiciIkkI 
• iflcr- pnuiiix' uf ;;ii an>\V('i- t(i the (lucst ion a^ to the 
I'clatid.. Iictuccii the c'fcctivc (Iciuaiid p'icc and tlio 
supply of 'he (•(iiniiKiility. 



riic chief diliicul lies in the computation of statistical 
laws of demand are due to ciianfies that occur in the 
nri.rket diiriu^i the period to which the statistics of 
prices and of (|uaii*ities of commodities I'efer. In order 
that the siatistical laws ,,f demand shall have suflicient 
validity lo <i'y\i- a- pi-e(li( tion foiniula', the oliscrvations 
nrist lie numerous; and in oi'der lo ohtain the re((uisite 
luuniier ot oliserx at ioiis. a consideralile period must he 
coNcred. This usually means that, during- the interval 
sur\-eyed in the statisii(al sei'ies, important chauf^i'S 
occui' in t!ie condition of ih.e market. But in case 
ot ^taple conunodities, such as the aKriculturai products 
with which \\v shall have to deal, the effects of those 
chaniies in the condition of the -narket that ohscure the 
relation lietween prices and amounts of commodity may 
he l.'iriiely eliniin.ated. As far as the law of demand is 
coiicei-ned. the principal dynamic effects that need to 
!i" con-idered aic clLaniO' i.i the volume of the com- 
modity tli;it ai'i^e from the increasinjr pojiulation, and 
chanjics in the lex,.] ,,f jiri-es which are the comhined 
result ot cause> >pe( itically re^poiisihle fdi- price cycles 
and of cause> that produce a secular trend in prices. 



I'lii Ldic i>f Jj( iiKinil 



69 



The cITccts of tlu^sc two t'uiiil;iinclit;il <'lKUi(ics may 1)0 
"liiniiiatcd ai)i)nixiinat('ly liy a single si;itistical device, 
namely, l)y deducing: tlie law nf demand from a gen- 
eralized treatment of the elasticity of demand. 

The decree of elasticity of deniand. accordiiip; to the 
ch'ssic formula, is measured l)y the nilio of the relative 
change in the amount of the <'om!no(lity tiiat is hoiiglit 
to th" relati\-e change in the i)rice per unit of the com- 
modity. Sui)i)ose, now, that instead of n>stri<'tiuK 
this conc(>ption to infinitesimal changes m pric(> and in 
amount of i -mmodity, we extend it to the finite changes 
that actually occur in the market. Then, th(> relative 
change iii the amount of commodity that is liought 
may he correlated with the n^laiive change in the 
c()rrest)onding price, and the r(>sulting appropriate 
regression e(|uation will gi\(> the statistical law of 
demand for the commodity. By taking the relative 
cliange in th(> amount of the conunodity that is de- 
manded, instead of the absolute ([uantities, the efl'iH'ts 
of increasing population are ap|iro\imately eliminated; 
and by t;iking th.> relative change in the corresponding 
l)rices instead of the corresponding absolute prices, the 
errors due to a fluctuating general })rico level are par- 
tially removed. If the observations shoidd cover the 
jjeriod of a major cycl(> of prices, and the commodity 
under inv(>stigation should be a stajile conunodity such 
as the repres(>ntative agricultural i)roducts with wliioh 
we shall have to deal, the above method of deriving the 
demand curve will give an extremely accurate formula 
summarizing th(> relation between variations in price 



70 



F.vnnoniif ('ijrhs: Tlnir Lnir and Cditsr 



and \-..rlati()ns in the amount of tlic coininodity that is 
(l('inaii(l('('. 

Tlic niclliod may l)c illustrated liv dcriviiifi the law of 
demand for corn. In Talih* I of the Appendix to tliis 
(•ha])tcr are reeordrd, for the period of IStKi Kill, in tlie 
I'nitod States, the ([uanlities of corn annually jiro- 
duced, th(> eorresp(;ndinj: prices per hushel, the relative 
ehaiif^es in the (luantity i)rodueed and the relative 
eluuifies in the price per husliel. If the correlation of 
the relative chan^ie in the amount of corn that is pro- 
duced and the relativ(> ehaiijic iti the eorrespondiuji, 
price per luishel of corn is assumed to he linear, the 
coetricierit of correlation is /■ = .TMI, and the equation 
of rej^ression is // = .SSOtu' -f 7.7'.l. the orifiin heinti .'it 
((>,()). iSc(> I"it!;ure 10.) 

In 'rabies ' II, III, ]\ . of the Appendix to this 
chai)ter, similar data are fjiven f(.r hay, oats, and 
potatoes. 'l"ho coeliicients of correlation are, for 
hay, r =- .71-"); for oats, ;• = —.722: and fo,- potatoes, 
/■ = — .S,")(). The regression (■( [nations aro, 

for hay, /y --= - .7()4;5.r+o.()l ; 
for oats, // = 1. 04 r),").r 4- <i.'.K^; 
for potatoes, // = 1 .21',l4.r-f 10.7"): 

the oripin in all cases being at i '*,<)). 

'J"he high coeflicicnts of correlatii.n that ha\e just 
boon given were obtain(>d on the assumption that the 
correlation between relative chang(> in aii'ount de- 

'Thc'latiidf tl.c Tahlfs I, II, 111. IV wcr.' tak<ii frmii the Yair- 
liiiiif: of till' Dcjiartinciit of Agriculture of tin I'tiitcd Siatrs for 
I'Jll. 



The Lair ,)/ Dondiid 



71 



.?/ 


• 

,1 















— - 


I, 



1 


1 


















i 


, 












»• 


•w- 














3 
■a 




A> 


k •• 


• 










i''^ 




VA\. 


















VV-' 










^ 






\ -aI 






t 








V- K 








»■ ., 






, 


\\ 








^"'-' 
% 








"^. ^ 


"N 


tSv 


















Vv 


















\\ 
















V 


V 


N 


-TS 






— — 













^ 



Pe'cfntafe chanfe m the producfij-J J' cj'--^ 

KKaiiK. Hi I'hr law if ili'imiiiil for iMrii. 
y =-.sviii.r + T.T'.i, iiriciti at i'^ Ol. 



I I 



>' 'I 



I i 

I 
if, 
I 



72 /■'(■ntni/m Ci/ch'.^: Till ir I.tiir <iii(l ( 'aii.sr 

iii;in(lc(l .-iiiil relative cliaii^e in jn'iee is linear, ^^'e shall 
see later on liiat t!ie twn varialiles are even i.nre 
intimately assieiated than wmild lie sujrui -ted hy the 
hitili eoetlicients of enrrelalinn. .hist ii we v. i<h to 
kiinw the fiiriu nf the law of demand wlien the resi-ic- 
tinn in\nl\-ed in tlie assunijjtion of linearity oi refir. s- 
sidii is removed. What will tie tli. >tatisiir;d laws of 
di'inaiid for the reproentative . (rinnioiiiiies c n, hay, 
oats, and potatoes, if the regression of rejat vo chanK* '» 
price upon relative chaniie in (luair ly ot commodity is 
assumed t.i he -kewand of the t\pe;, a+/u--f j' + f/x'? 
The (|ue-iion i> answered liv httinii, ace lin;i to the 
.\Ietlio(l of l.ea>! >(iuares. tiie e(|U:ilioii // - (t +Ikv-\-cx--^ 
(if to the data of Taliles I. II, III, 1\' of the .\ppendix 
to thi> cliapter. Tiie re>ults of tli< computations are 
oxhihited in Fijiures 17. 1^, I'.i. I'U of the text . 

The statistical law- of demand for the commotlities 
corn, hay, oat.-, and potatoo pre-cnt the fiuidamental 
characlei'i-tic which, m the classical treatment of de- 
mand, has lieen assumed to lielonji to all deni.and 
curves, uaniely. iliey are all ney;atively inclined; tha' is 
to say. >pcakinji from the ; oint of \ iew of axcraf^e 
re-ults. "the tii'eatei- the amoiuit to lie old, the smaller 
will he tlie i>rii'e a! whidi it wil! find |)iirchasei's. or, in 
other words, . . . the ,am<iunt demanded increas(>s 
with a fall in price and dimiiushe- wit h a I'i-e ii\ price." ' 



' M:ii-li;ill; I'idiiiph ^ iif Erithiiiuics. Itli edit., \\ '"'• ''i ciisc i^f 
tlir lau iif (Icii Mini fur |i;i\-, tliiir i< -a slij^lil ilpwanl llirii at (he e.\- 
ltrniit> iif ilic ciiiNr. Till- is iluc to eiic ixtrciiic (ihscrvatii)ii, aiul 
tlic xariatinii is not a simiilicaiit i'Xci'i)tioii to the aliovc pc'icral rule. 



Tin: Lniv <>J Donand 



73 



5. -J 









f,-. 



*^-« 



















\ 
















\ 

■ 













































1 






(1 














"^ 


K^ 
















\_ 




V 




\ 
















N 


■^ 
















\ 


































-* 


5 


*A 


1 * J 


9 »3. 


* »^ 


9 .dl 


^ 



Per^ -ftfade chsnde m the production ot^ corn 

Fici'UK 17. Tlic liiw of ell ii];ni(l for corn. 
.94 — l.OS'J'ir + .023911'— XM)2'i\x\ oiigin at (0, 0). 



I 



H 

n 

H 

i 
n 






vW 



:l 



■La^'-Tii 



74 



Economic Cycles: Their Law (ir.d '\iuae 



'SJ 






^ 





















1 








































\ 


7^ 














V 










1 






\ 


V 
















^^. 

N 


A 
















^r 




















— 


































Perec 'd* chan^r ji the prQdi.cf,on of hay 

FiiiUHK IS. The l:iw of (Icmaml fi>r Iwiy. 
= 4,17 — .0-4tW)x — .(M)77()j' + .()()<):iS.-)j->, oriniii at {0, 0). 



The Law of Devmud 



75 



<•*. 



>< 



^ 



1 1 ^^^^ 



Percentage change m the p> aduct'on c^ oats 

Figure 19. Tho law of dcnmnd for o&ts. 
y = 8.22— l.llMMx —.0000;^* + .00()27?i', origin at (0, 0). 



I'M 



H 



7(1 F.rouditiir Cj/clis: Thrir Ldw anil ('uiisr 





\ 
















1 A 

































1 




\h 
















\t 
















\ 






























r 









^ 










L 








1 


V 


>o c 


K 


- - — 


^ '- 










•^ 


«.-< 














^ 


\ 






1 















V = 1.7 



P'ercfntajje charter m the production of potatoes 

FiouRK 20. The law of ■Idiifuid for |,iitatoo.s. 
' — '.5()t(2x + C-Msori" - .(KH)i(t7r\ (irinin at (0, 0). 



Tlif l-iiir of l>i iiiiiinl 



77 



lint iiiiliki' the cIhs-'k'hI thcMiv of (IciikiikI uhirli \v;i> 
limited t«i tlir ^iiiiplc i'Iiiiiiim;iI inn of thi> niir cliaiactcr- 
i.iic, (ff/'C/'N luirihiis. the -t!iti>tic;il l;iw> tli;it liavc just 
|,rcli derived apply tn the aveiatie eliallU"'- lli;i' sneiely 
is aetually uii(ler(i'>iii^. They Miniiiiaii/<' the ehaiincs 
in prices that are to be expected li'Hii < haiij^es in the 
supi)ly nf the coniinodity. thus eiiahlint!; niie to |)redict 
ttie prnlial)le variation in l>riee ttiat will h.llow ui)oii an 
assiKiii'd variation in the amount of the eonunodity. 
They exhibit the eomiection nf prol)aole result> not 
only in a (lualitative l.ut al>o in a (piantitative form. 

Till I'mlii-lin.i t'f I'rircs 

It has been said that the statistical laws of demand 
rnable the economist to i)redict the i)robable variation 
in i)rice that will follow upon an assigned variation in 
the (luantity of commodity that is to be sold. IIow 
accurate are the results of preitiction that are liased 
U|)on th( slaiislical law of demand? 

The accuracy of the i)redi(tion in th(> case of any 
given commodity will vary accordinj;; to the det^ree of 
fit of tlie type of curve that is assumed to represent the 
relation between the relative cha.igc in price and the 
relative change in the (luantity of the commodity. If, 
for oxami)le, th(> eonunodity in (luestion is corn in the 
United States, and the type of demand curve is assumed 
to be linear, then, according to tlie results in foregoing 
l)ages. the correlation between the two variables is 
r = — .780, and the regression eciuation is // = .8890/ 
+ 7.79, the origin being at (o,o). (Figure Hi will facili- 



i 



m 
ill 



78 



lu(iiiii//nr Ci/chs: Th, ir /.(///• uml ('nusf 



tati' tlic (li>cti^siori <it' the cmx'.) Hy iiM-aiis of tliis law 
of (IctriaiMl it i> pn»ili|(« to Ill-edict tlic prolialilr cliaiiHf 
ill tlw [nice tlitit will follow upon a f^ivcii cliaii^ic in 
the (|iiaiitity to I.e -o|,i. jn i<.)| j. m the I'nited States, 
tlie <(iiaiitity of corn jiiodiiced was _',.').■{ 1, 4SS, ( () 
')iisli('!s, and the mean farm prii c on Decemlier I. i'.tll 
was (i:.S cents. In l!t|_' tiie i|uantity of corn pfoduced 
was ;^1-M,71(;,(l()(li.ushe|<; what, then, was the prolial)!«" 
price of corn on l)<'ceinlier 1, P.tlJ' 'I'lw percentan(> 
• •haiitce in the (lu.antity jiroduced was '2:\.\\. Siih- 
stitnte thi- \aliie for .1 in the foriniiia for the law of 
<l''niand '/ .SS'ICm- f 7.7l», and >olve for llii- value 

(it //. It is found that the proli.alile change in price would 
l>e a fall of l.'i.Oii per cent., which, since the puce in 
lit!! wa> til.s ceiit>. would mvv .VJ.7 cent> ;is the prolt- 
!il)le |)rice for Decemlier 1. iltlJ, whereas the actual 
I)rice was }S.7 cent-. 

According; to ; he theory of linear correlation, the 
accuracy 01 the n>rrcs<ion e(iuation as a iirediction 
formula is measund liy N = o-„ ^ 1 - r', when- /• is 
the coelli( lent of correlation hetweeii the variables, 
^^ is the -(aiidard de\iation of the variable // about 
its mean value, and N is the root-mean-s(iuare devia- 
tion ot the actual observations about the regression 
line; or. in other words. N- is the mean value of tho 
mean-s((uare dexiations about the regression line, of 
the obseivations in the .-everal arrays of //'.-.-. I''roni 
the 'I'able of the l'roi>ability iiitepral it is known 
that in a symmetrical distribution of observations 
about their mean vali e, tiS per cent, of all th- observa- 



Tin l.llir III I >■ "IHIIll 



79 



(inri^ full witliiii ± the r<>(.t-iin'!ill-sqii(in' dcviiitidii of 
the «il)MTv;iti(iM> fn>iii i|i. ir mi'jiii \:ilii<'; It.') per cciit.. 
l.j.tuiMMi ± Iwicr thr i:!i(t !;ii'i!i— ((Uan- (Irviatioii: :mi| 
'.•'.•.7 per rent. lictwiTH -*- lhrr<' tunc- tlic n>i)I-riic:iti- 
>(|U;in' (Ifvialinii. It i- tlirr; lore pM-.sil)l.-, Wy mciiis 
III" the j'roliaMlity liititMal to ;iili\ the dciif'c nf pnil)- 
altility t'lat a dcvial khi -liall fall witliiii any uivcri 
multiples nr -iiliiiiiiltiple- of the fiMit-meaii-scnian' 
(levialidii. In <'a-i' of the ii<e <>f tlie linear law of (!<•- 
maii<l for eoni in ilie riut.il State- as a prediction 
forniiila. the root-mean-siiuare deviation of the oh- 
servatioiH ahou: t lie deiiiaiid curve was N "■,,n 1 -r-' = 
!.").'.t'J per cent. That i- to -ay, if we asstnne the law of 
demand that was liased upon oliservations from ISI'iti 
to i'.ti I to hold in I'TJ, then it is <.».'i to o, or l".t to 1. that 
the percentafie variation in the actual price for I!!!"-* 
from the pereentaH'' variation a- calciilateil from the 
law of demand will he hetween ± 2 i l.").'.»2i, or .'51. SI 
|)er cent. 'I"he calculated percentaiie chan(ie in the 
price for 1!II2 was a lall of j:{.(M. per cent.: the actual 
fail was 'JI.'JO per cent., giving a dilTerence of 7.14 per 
cent. 

The i)r('cision with which the linear law of demand 
may he used for the iJnMliction of the i)rice of corn in 
the I'liited States jnstihes the belief that for some ])iir- 
po.ses it is iinn(M'(>ssary to seek a greater degree of 
accuracy than is afforded hy the simple linear laws. 
Hut it is well to lu> atile to reach tho maximum degree 
of precision, and for this reason wo have fitted, to the 
data of the Tables in the .\ppendix, the more coinplex 



■•■ !-; 



ii:l 



m 



m 



MICROCOPY RESOLUTION TEST CHART 

ANSI ond ISO TEST CHART No 2 



1.0 



I.I 



U2 "■■ 



M\ 



2.5 
22 

ZO 
1.8 



1.25 



1.4 lillt 1.6 



^ .APPLIED INAHGE Inc 



80 



lu'iiniitnn' Cijdcfi: TIni,' Ldiv iiml ('nii.<C 



curves // =(1 +h.v->rr.r" + <I.r^. the graphs of wliicli, in casp 
of the rcprcsciilat i\(' co i nKKiitirs corn, liay, oats, and 
potatoes, ai'e ^i\en in l-ijiui'e,- 17. 1'^, I'.t, 'JO. What is 
the fi.'iin in i>reci>ion when the more complex curve is 
vul'^tituted for the simpl(; straijiht line? The scatter 
of the ohseivations al)out tlu^ >lrai^ht hue of rcj^re-sion 
was measure<l. a whilo ajjo, l)y taking the root-mean- 
s(iuai-e deviation of tlio observations about the lino, 
tliat is, i)y u>iufj; S=(r^\ 1 — r'. In order to compare 
with this result the distribution of tht! observations 
about the more complex curve, y =(i+hx+cx'--\-<lx'\ 
the distribution about the latter curve will likewise l)e 
measured by the root-mean-scjuare deviation of the 
observations. In the littk; table (rWrn below, t!ie 
measures of scatter of the observations for the two 
types of demand i urves are presented in a form that 
will make comparison easy. 



ScATrr.u OF Ouskhvations Ahoit iuf: Law ok Di-:mv\I) 
J{oot-Mp:an-Sqiaue Deviation ok (Jbskuvations 




\\'licn tii(> rcjire: 
sion is liuciir 



\\'lu'!i tlic rc<j:r('<- 
sion is skew 



].") (t2 per 


Cl'llt. 


7 M'l J1IT cent. 


\) n.i •■ 


" 


4 ()."> " " 


10.02 '• 


i( 


10 17 " " 


21 2'.» ■• 


" 


1) (|j •• '< 



Tt is clear that in al! cases a pain in precision is ol)- 
tained by using the more compk'x curve. 

Before iea\ing this to])i(' a I'cniark .^houkl In- made 



Tliv Ldir of ])( i/Kind 



81 



tli:i1 has a l)oai'inp; ui)on the (t priori theory of dcinaiul. 
Ill ti'catiscs on i)uiv ccouoinics. !)articularly in thox' in 
which luatlu'inalical analysis is ciiiploycil, the iiiaslors 
of tlio (I priori iiu'tliod point out wliat they rcsanl as 
the cxtrciiic (liflii'uhy of tlic actual prohlci" of the n>la- 
tioii of price to ([uantity of coniiiiodity a difiiculty 
growin"!; ou» of the interrelation of the many factors in 
the i)rol)lein. If, to limit the illustration to a simjile 
<"isc, one wishes to know how the price of corn is re- 
lat(Hl to the (juantity of corn that is produced, he is 
told that the proi)Ieni is inextricably complex: If there 
is a deticiency in corn, then hay, or potatoes, or oats, 
or all three may he substituted in part for corn, and con- 
sequently the variation in tli(> price of corn that fol- 
lows ui)on a (l(>ficieuey of corn cannot be traced with- 
out knowing in what degree, wlien the price of eorn 
varies, hay, oats, and potatoes are used as substitutes. 
But this is not all. The degree in which hay. oats, and 
potatoes are sul)stituted for corn is dependent not only 
upon the price of corn but also on their own several 
prices, and these latter jirices are, in turn, dejjendent 
u])on the supply and price of corn I This statement of 
the problem, coinjjlex as it appears, is unduly simpli- 
liediand it is jiresented not in ord(>r to ridicule the work 
of the masters who have elaborated tlie method of 
stating the problem in tlie form of simultan<>ous ecjua- 
tions, but to show how hopelessly remote from reality 
is th(> very best tlHH)retical treatment of the j)rol)iein 
of the relation of })rice to the {[uantity of commodity, 
and to suggest, from the results of the ureceding pages 



<S1 



Kciihiiiniv Cjjrlts: TItiir Liur int<l ( duf^e 



of this rhtiptcr, liow iini'siiiary, thcnn'tical (linicultics 
iiro (lis[)('II('(l l)y sdlviii^ roal pri)l)l(>ms. 

Of cduisc it is theoretically possible when there is a 
(loficieiiey in the produetion of corn, that oats, hay, anil 
potatoes ;ii;iy he sulistituted in part for corn, hut in- 
stead of conjuring up these and other possihilities that 
ar(> never tested, would it not he wise to ascertain first 
just how closely is the variation in the price of corn 
related to the variation in its own sujiply'.' When the 
statistical nivesti^:ation is made and it is found that 
the correlati( coefiicient is r = -.789, and that wlien 
a skew relation is assumed insteail of the usual linear 
relation, the coiuiecticjii hetween the variables is still 
closer, one sees very clearly, if our illustration is a 
typical case, that for ni>)st of tlie prohlems of actual 
life, it is unnecessary to face th(> comjilex ])ossil)le in- 
terrelation of plienoineiKi contemi)lated in th(> theoret- 
ical treatment. l"or th(> sake of (H'ononiy of time and 
of talent, th<>oretical and statistical work sliould ^o 
hand in hand. Iacii tlie c((mpl(^x theon^tical jirohloni 
that has just iieen sketched may l)e toted as to its 
hypotheses and conclusion by the statistical method 
of multiple correlation. 



Klasticitu of Di'inand 

The coefiicient of the elasticity of (l(Mnand for a 
commodity has been descrilu'd as tlie ratio of the rela- 
tive chaiijie in the ([uautity of tlie commodity demanded 
to the relative chanjie in the i)ric(>, when the relative 
chaiif^es are infinitesimal. Starting with this descrip- 



Till' Ijiir of Dtrnand 



r,3 



tioii, wo aro !il>l(\ hy moans of tli(> laws of (Icinaiul for 

tlu' several eoiniiiodities, to measure their resix'ctive 

(lefinusof elasticity of (lemaiul. It will he recallcil that, 

ill the form in winch the laws of (leiiiaiid have I ecu 

preseut(>(l in precediiiK Jtafies, the variable j* has he<'u 

taken to represent me relati\e chanf^e in the ([uantity 

of the eonimodity, and tlie variable //, the corresponding; 

r<'lati\(> change in the price. 'V\\v coefiicient <f the 

tlx . 
elasticity of demand, therefore, is e(iual to j^ when .r is 

zero. All that is n(H>ded to obtain the measure of the 
deforce of elasticity of demand is to differentiate ;/ witli 
respect to x in the e(iuation to the law of demand, 
place J = zero, and then take the reciprocal of the result. 
The method may be illustrated in case of the four 
representative commodities, corn, hay, oats, and pota- 
toes. The law of demand for corn see risure 17 is 



Therefore, 



y --■■ .94 - 1.()899j- f .02.S91j-2-.000234j» 
''' l.()S99 + •2(.()2:591).r - :H.(K)()2:54)j^ 



dx 



When .T = 



(is 



-1.0899, 



(!X 



1 
1.0899 



.02 



and conseiiuently the coefiicient of the elasticity of 
demand for corn is —.92. Since the law of lemand for 

hav is 

y = 4.17 .94()j- -.0077j-= + .000385x» 

JJ = -.94(1 when X - zero. 
dx 

and the coefficient of elasticity of demand is — l.(H). 
For sunilar reasons the degrees of elasticity of demand 



[(..- 



84 Kfiiniunic Ci/chs: Tin ir l.dir ami ('nii!<e 

for iiats ;ni(l lor iiDtatocs nvo respect ixdy, --.S4 mikI 
- -.(iii. 

In ohtainiii^ these niitiierie:il \;ilue.- tor the (■(lelheient 
of <'l;tslieity. the laws of deinaiHi for the respective 
ei-ops Iia\-e lieeii as-uiiied to lie pai'aliolas of tlie tliird 
order. If the liiieai' laws of demand had been taken for 
the purpose, the coeilicients of elasticity would l.ave 
been diiferent. I'or example, the law of demand 
for corn see l''i^ure 1(1 is // ==- .SS!)ti.r + 7.7!l which 

would ^ive '/'^ - - •^^■•'■|. or ^^■'= -1.12, whereas the 
coeflicient was - -.'.»2 in case of the more comi)lex curve, 
'i'his disci'epancy lietween the results when diiferent 
types of cur\-e> are used for the demand cur\-e shows the 
need of care in drawing conclusions that are ha.sed upon 
munerical \alues of the coeliicient of elasticity. The 
discrejiancy does not iinalidate the method. When 
diiferent measures of dcjrrees of elasticity .are atfoi-ded 
by different types of cur\-es. there is a peru^ctly satis- 
factory criterion which makes it possible to d(M'ide 
between different cot'llicients of elastici'y: The coefii- 
(■i(<n1 is to be jji'eferred which is deduced from the de- 
mand (au-\(" that fits the data with the hijil'cst decree of 
probability. Th(> demand cur\-e that tits best the data 
affords the best measuiv of the deji;ree of elasticity of 
demand. 

The conchi-^ions of this chajiter may be briefly sum- 
marized. In th(< closin,u; ((U.arter of the la>t centurv 
great hopes were entertained iiy economists with 
regard to tlie cajiacity of economics to be made an 



Tlic I.ini' (if Ui ttidiid 



S.") 



"exact science." Accunliiiu: to the vi:'\v of tli(> foremost 
theorists, tlie (lexcloptiieiit of the doclriiies of utility 
and \ahie had laid the foundation of scientitic economics 
in exact concejjts, and it would >oon i)e |)ossil>le to 
erect ui)nn the new fotuidation a firm structure of 
interrelated parts which, in deliniteness and cofjency, 
would he suflKcstive of ihe se\('re beauty of the 
matlien.atico-physical scicmces. Hut this exju'ctatidii 
has not been realizetl. On the contrary, faith in the 
jiossibility of an ade(iuate "exact" treatment of tlie 
science has proj!;re<>ivelv diminished, and interest in 
economic theor\' in jieneral has decidedly lost {iround. 
'["here musi have lieen somethin<i fundamentally wrong; 
with the traditional handliiifi; of the subject, for cer- 
tainly it must be admitted that the i)arts of a science 
most worthy of study are precisely those jiarts which are 
concerned with the g:(>neral and the universal. Why, 
then, should tliere have been the jiradiial dissi])ation of 
interest in theoretical economics? 

'l"h(> explanation is found in the ]>rejudiced ])oint of 
view from which economists regarded the juissibililies of 
the scienc(> and in the ratlically wronfj; method which 
they i)ursued. It was assumed jiratuitoiisly that 
economics was to 1h> modeled on the simpler mathe- 
matical, i^hysical sciences, and this as>timption created 
a ])re,iudice at the outset both in selectiiifj; the data to be 
investigated and in concei\injj: of the types of laws that 
w(n'e to be the object of research. iM'ononiics was 
to be a "calculus of ])leasure and pain." a "niechanics of 
utility," a "social mechanics," a "physique sociale." 



86 



I'AOiKimic Cycles: Tin ir Lnir (iinl ('ansf 



The l)iaso(l |)()int of view implied in flicsc (l('scrii)ti<)iis 
lod to an uikIuc stressing of those aspects of the science 
which seeiiietl to hear out the pretentious metaphors. 
One would naturally suppose from this manner of 
conceiving the science that the economic theorists 
would at once have entere(l upon their task with the 
methods that ha<l proved themselves useful in the 
physical sciences, liut this they did not do. They 
seemed to identify the m(>thod of i)hysical sci(-nces with 
e.vperimentation, and since, as they held, scientific 
experimentation is imj)ossil)le in social life, a special 
method had to he tlevised. The invention was a dis- 
guised form of the classical rirkris pdrihus. the Tuethod 
of the static state. 

The point (tf view tliat has been exemi)lified in this 
chapter is that the facts in their full coucreteness must 
never he lost from sight ; that the laws which are sought 
are of necessity, at first, proximate laws, laws that 
obtain in full empirical reality, and are miuins if arriv- 
ing at laws (,f larger gen<>rality; that the method to be 
folloW(>d is the method which makes progress from the 
data to generalization by a progressive synthesis — 
the method of statistics.' 

' With regard tii the iiictlKiclolntiy cf tlic sorial sciences, the 
writhigs of Couriiiit are always lielpful. Tlie fdUowiiig quotation 
is taken from a treatise pulihshed thirteen years after his eisoch 
inakinjf Ihrherchts aur /e.s iiriiicipi.s matheinatiquen dc hi thcork des 
richexsei^. 

Si nous re.stons dans Tonhr des causes serondaires et de.s faits 
(ihser\-ai)les, h- seul au(i\iel hi science jiuisse atteindre, h'i thoorie 
iiiathenialii|ue du lia.~ard . . . nous apparalt coninie I'apiihcation 
hi phis \aste dv hi srienee ihs noiiihres, et eelh' (pii justilie le mieiix 



'/'/((' Ldir <if I)( DKUid 



S7 



Sfartintj; with this pn\n\ nf view and i)iirsuiiin the 
iMcthnd that lias ju>t hccr. (Icscrilicd, we hav(> attacked 
the old i)n)l)l('m of the form of the law of demand. We 
have ol)taiiied the concrete laws of demand for repre- 
sentative commodities, have aflixed the decree of preci- 
sion with wliich the laws may l»e used as formula; for 
predi. tinu; i)rices, and ha\c measured the elasticity of 
demand for the respectis-e commodities. 

Ill all likelihood it will he said Uiat what we have 
achieved is not exactly what the jiartisans of the metliod 
of cccteri.^ paribus i)roposed. To this criticism we reply 
that their inunntidtc prohlem of the relation of price and 
quantity of conunodity, cai>ris lutrlhus. was vaguely 
conceived and actually ahaudoiied hy those who >oufz;ht 
to sive it definiteness. as heiiig incapahle of concrete 



railage: Mitinliini Kgimt niinmi. V.u cITct, quciiciu'cn aiciit | (•ii>^' 
fcrtaiiis jiliilosoplics, ficu nc nous autoiisc i\ cnjirc (lu'en i-tii.^.-c 
roiidre raison lii" tens Ics iiliciKJiiiiMic.'* avc Ics notions (ri'tciidnt', dc 
teinl)S, do niouvciiicnt, en \u\ met. avcc Ics sciilc.^ netioiis dc^ fiiaiid- 
ciirs rontinncs sur l(s<iiulk's ixirtcnt \v^ nic-urc- ct Ics ralculs dti 
g6uiiietrc. Lcs actcs dcs i-tics vivaiits, iiiK !lif;ciits ( iiKnaux iic 
s'cxi)li(iuciit inillciiiciil, dans I'ftat dc nos connaissanccs, ct il y a 
do bonnes rai.sons dc rnjire ((u'lls no s'cxiilitiucront jamais jar la 
niC'('aiii(iuo ct la KC'oinctric lis no toniliont (h.nc point, ] ar lo coto 
gooinotriiiuo on niocani(|iic tlans lo doinuino dcs noinliros, nuns ils 
s'y rctrouvont pla(\'s, on tant <nio los notions do oonilMnai.-^on ot do 
rhanco, do oaii.so ot <k' liasard, sont suiioriouros, dans I'ordro dcs 
abstractions, :\ la ni'Minictrio ot iV la niooani(iiio, ot s'aiipliqucnt aux 
phonunidiios do la nature vivanto coinnio ii ooux ([uo iiroduisont los 
forces qui sollicitent la niatioro iiuircanicino; a\ix ados roflocliis dos 
etros lil)ros, ccnuno aux d<''torniinaiions fatalos do ra|)!iotit ot lio 
I'instinct. 

K.<sai atir /o.s ftindonriits ih ikis ninnnissdiicc tt sur /<^ nm.rtfrrs 
ilf Id criiiiptc pliil(is(i]>liiqur. vol. 1. pp. (Vl-t).'). 



^^ I'j'iiiiiiifi/c Ciici s: 'I'liiir l.nir nnd ('dilf 



sc 



Miliitin'i: tli.-it uhcii ilic priililciii i- clciirly >l;itc(l. it 
;i(liiiil-- i.r Milui iiin li\ II II 'Mil- III' ;i nictlidd w liidi we liavc 
indicated, tlic incthnd nl' iiiuliiplr rurrclat ion ; and that 
what we lia\c aciiicxcd i- tlic -Dhitinii of their iillnndlr 
jifnlileiii lit the I'elatidii of price and ([iiantity ut' eniii- 
iiinditx in a d\naniie -neiet\'. 



AIMMADIX 



tahm: I I 



III rilMDI ( IHlN AM) IHl; 
r.MlKB .*^l M I -^ 



OF f'nIIV !\ TMK 







AVEHAI.I 


i 

1 






PnMtiriri-tv or 


F»HM I'm. » 


I'fK. rvr»iiit 


r>:n') N 1 ^■. . 


\ k:An 


(*1IHN IN Ihim - 


I'kr Hi «iiki 


<lHN<iK IN 


flUN'.) 1 . 




KANUHUt Bt.BUISI> 


Dt.t'EMUKII 1, 


i'KllUfCTIUN 


Cku I. 




1 


IN Cents | 






I'^til'i 


s(i;.<t4t> ' 


47 4 






l^<i7 


7t>s.:fj() 


.-.7 


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+ 19.41 


1m;> 


'.MH1..V.'7 


40 S 


+ 17.99 ! 


— 17.H9 


iMi'l 


s7»,:iJ(t 


.-)'.» . s 


— 3.55 : 


+27. 7H 


1^7(» 


i,(i*.it,J."i.'> 


4'.) 4 


+25.15 


—17. Hit 


isT 1 


'.I'.tl.s'ts 


4:5 4 


- 9.33 


—12.15 ; 


ls7_> 


l.i»'.ij.71'.i 


:ir> ,i 


+ 10.17 


—18.00 1 


IsT.i 


'.i;ij,'.'7i 


44 2 


— 14. OS 


+ 25 21 


ls71 


.s.-,i(,US 1 


r)S 4 


— S,M 


+ H2 13 


is;.") 


i,:vji,(Hii> 


■M\ 7 


+ .-),■) 3'.) 


37 10 


Is7ti 


1 .'Jsii.S'JS , 


34 


— 2 s2 


- 7 3t> 


|s77 


l.;U'J..'l."lS : 


;u s 


+ 4 .-)7 


+ 2.35 


ls7s 


l,:iss;.>i'.i 


HI 7 


+ 3 40 


- H ill 


Is7'.l 


l,")t7,'.l()J t 


H7 r, 


+ 11,^0 


+ 1S HO 


1 SSI I 


1.717.»:i.-) i 


HO () 


+ 10 95 


+ 5 00 


Issl 


l.l'.U.'JIil 


t)H fi 


—30 42 


+ 0(1 til 


1S.S.' 


i.t; 17,1 ).'.■> 


4S 5 


+ 35 33 j 


— 2H 71 


iss;; 


1. .'■..') !,IM17 


42 4 


— 4 (W 1 


— 12 5S 


Issl 


1.7(t.'...V.>s 


■Ar, 7 


+ 15 70 


-15 so 


Iss," 


1 '.•:«■). I7t( 


32 S 


+ 7 S3 


- S 12 


ISSli 


l.HC.'i.lU 


30 ti 


-13 its 


+ 11 ."it 


l^s7 


l,l,->f.,lf,l 


44 4 


- 12 .")7 


(21 HI 


|s>S 


l,',ls7.7'.M) 


3» 1 


+ 30 51 


-2H 20 


lsS',1 


•.Mr2.si.t.' 


2S 3 


+ 2it 


-17 01 


Is', to 


l.»si.t.U70 


:>() 1) 


— 2it 4S 


+ 7S so 


Is'll 


•J,l)tW),l.-,4 


40 


+ 3S 27 


— lit 7(> 


l.s'.)2 


l.HJs,4f4 


39 4 


—20 it") 


- 2 ilO 

- 7 H() 


1S'.»3 


l.iU'.t.tOii 


3f. .'•) 


— 5.") 


l,S'.t4 


1. 212.770 


45 7 


-25 11 


+25 21 


1S'.)'> 


2, 1.') 1.1 Hit 


25 3 


+ 77,37 


-44 (il 


ISOt) 


•J.Js:{,S7.') 


21 5 


+ (■) 17 


-15 02 


ls'.»7 


l,',102.',>l'>s 


20 3 


1 -10 (is 


+22 H3 


LSI IS 


l.'.fJl.ls.-. 


2S 7 


+ 1 11 


: + <t 13 ! 


IS'.i'.l 


2.07S.114 


30 3 


+ S (HI 


+ 5 57 ^ 


IIHH) 
1!M)1 
I'.IO'J 

l'.M»:{ 


■J.lO.'i.lOH 
1, .').'■.'. .VJd 
■2..7.M,(US 
2.2 1 1.177 


H.") 7 
t)0 5 
to 3 
42 ."i 


+ 1 HO 

— 27 (i7 

+ 05 75 

-11 07 


+ 17 s2 
! +tiil 47 1 
! -HH.39 ; 

+ 5,40 


I'.IOI 
I'.tO.i 


2,ttl7,4sl 
2.707.i»!t4 


tt 1 
11 2 


+ i» it5 
+ it 7.") 


+ 3 70 
— 5S 


I'.HM) 
l'.»ll7 
lOOS 


2.'.V27.41i> 

2..'i',l2.:i20 
2, litis,!).") 1 


H',1 '.1 
.'1 f. 
00 


+ S 10 

11 1.") 

+ 2 (11 


— 3 10 

+2il,32 ' 
+ 17 44 


I'.MI'J 
HtlO 


2,772,:i7C. 
2,ssf,,2f.() 


."'.) 
!-> 


1- 3 Si) 
+ 4 11 


- 1 ti5 
— 19 40 


1 I'.lll 


2„-):U.lss 


f.l s 


-12 2it 


+2H . 75 



90 



Ia iiiiitiiin- ( ijili.s rill If I, 



tin- III 



,<l ( 



T\IU III T 



III l'l:"|il 1 I liiN KM) TUK I'llll K nK II M IN Tllf: 
I M I I I) St \ IKS 



PacioiriTiiiN or .\vkr.«(ir F*hm , 

IIav m Thiii- I'kh k I'kh Tux 
wANim i.r 'I'liN-* l>».<KWHkHl. 
I Inn ' JiNKilliK !<« Dm I tHK 



1)WH 
isr.7 

|M,S 
I Mi" I 

IsTd 
ls7l 
|s7i 
ISVI 
1S74 
1H7.-, 
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1n77 
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1S7'.I 

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ISM) 

lss7 
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IV.tl 
IV. IJ 

ls!»:i 

IS! II 
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1H!>7 
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l!HII) 
1!HM 
lltD'J 
l!Mi:i 

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I'M; 

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v.>m 
lino 
iini 



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is, 170 

ti.7:i2 
1 1 ,7!tr) 
ii.i.ni 
tii.i.i;! 
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47,444 



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lit 


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s 


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( 


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s 


lis 


s 


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li 
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<'mavm»; |\ 


C'll%>itlK IN 


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I'RK H 


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— 9 :« 


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— 9.51 


+ 5 ;m 


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4- 20 


— 4.71 


4-10 00 


— 9 72 


+ 10 74 


Hi 70 


4- 2 47 


li r,!i 


4-2.") 2:{ 


i:t !is 


-10 :i!t 


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r '(III 
2 s7 


Sj 


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f 12 ')2 


12 1 1 


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t !i !i:{ 


f .'i s,-, 


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21 ."iii 


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r 1 117 


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t 21 17 


—11 ').'> 


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+ .01) 


f 12 (iO 


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(- 2 42 


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1 00 


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— 2.29 


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—22 10 


+ 19 41 



I'hi I Mir (if l)i ma ml 



01 



TAIU.i: III The Pu(ir)i ition ask thk I'hk k of 0\t» in the 
rMTKD States 



1 




,1 

.\viH«ac ll 




1 


I'mitnrTi'iN or i 


K\KM I'Kirr ' 


I'KHirNTAllIC 


1'r.Rrr.NTtoB 


\ t \H \ 


Oath is Th'!! • 


I'KH lllKIII 1 


<'H*n »». IN 


('HtSOI. IN 


i 

1 
1 


atNlM Ur Bl'UIELK 

i 


llECEMBEn 1. 
I<« CiNTC 


r«<IUtCTI«N 


Hmi'B 


iMili 


2f.s.in 


:!.-, 1 






l>M.7 


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tl .'. 


+ 3 04 


+20 78 


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41 7 


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iM.'t 


2ss.:!:u 


US 


+ i:{ (10 


— K..S7 


isTn 


217.277 


■M 


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2.V.,7l;J 


:{<i 2 


+ :V42 


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2!t n 


+ (J 2tJ 


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1^7.1 


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:ti (1 


r>-i 


♦ 1.") 72 


is:i 


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11 ()'.) 


fM\ i;i 


IsT'i 


:t.-.j,:ns 


:i2 (I 


+ 47 41 


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\s:<; 


:t2u,ssi 


:i2 1 


— « 44 


+ 1 2.-) 


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:i:i 1 


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IssO 


•iiT.ss.") ; 


:tti 


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+ H 71) 


iNNl 


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4ii » 


— :m 


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1 sv_> 


»ss.2.'.l t 


:i7 .') 


fl2 i:t 


10 IH 


isvii 


:)7i,:iii2 


:i2 7 


+ 17 01 


12 so 


issj 


.■)S:i,C)2s 1 


27 7 


+ 2 It) 


!."> 20 

1 


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+ 7 ,s» 


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lS>t) 


t;2i.i:ii ' 


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s » 


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27 S 


+ li :i'.i 


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ISVt 


7.J1,.')1.') 


22 '.t 


+ 7 (Ki 


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ls;i() 


r)2;{.r,2i 


42 4 


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+sr> 1.') 


IV.Il 


7:is.;«u 


:ti r, 


+ 41 02 


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IV. 12 


(ici.o:!.") 


M 7 


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+ n:( 


l.V.l.i 


(>:i.s.s.").') 


2'.t t 


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+ ;i n:i 


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l!l !• 


+24 .">;{ 


— :{.s , "iS 


I.VK) 


7()7.:vi<> 


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tilts. 7(ls 


21 2 


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( i:{ :i7 


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7:ii).'.tii7 


2.-. .') 


+ 4 tiO 


+ 20 2.S 


Is'.t'.t 


7'.Mi,17S 


21 (t 


+ s.'Xi 


— 2.:j.") 


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S(H),12t> 


2.'. S 


+ 1 ii:} 


+ 3.1)1 


I'.HIl 


7:{t>,S(«» 


;{() '.1 


— S.04 


+.54 r>.'> 


1!M>2 


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;«) 7 


+:m 07 


-2:501) 


I'.to:! 


7M.(«ll 


;i4 1 


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; +11 07 


I'.MM 


S'.ll,.')!lti 


:u :i 


+ 14()<> 


1 — S.21 


1! !().'> 


'.t.-,:{.21i! 


2!) 1 


+ li .5o 


— 7 ()3 


I'.tO') 


'.tiit.'.iii.') 


;u 7 


+ i.2;i 


: + H.<i:i 


I'M 17 


7.-.4,ti:i 


41 :{ 


—21.81 


+:» 7.5 


1<MI^ 


M)7,l.".t) 


47 2 


+ ti.ltO 


' + 6.55 


I'.lO'.t 


I,(H)7,:<.'>:f 


40 ^ 


, +24 SO 


—14.10 


I'UO 


l.lst),;ui 


M 4 


' +17.77 


> — 15.()<) 


Htll 


<.t22.2<.»H 


4.")() 


i —22 2t> 


+ ;50.8l 



92 



E> 



cononiir Cija 



TJu'ir Ldir (I'lil Cause 



TAIU.i: I\', 'I'm; I'lidun Tinv and tiii: I'khi; dr I'oi moks iv 
iMi; I'm HI) Sim i;s 



IsHti 

lMi7 

Isr.s 
Isd!) 
Is7i) 
IsTl 
1S7-' 

is7.; 

ls7i 
ls7.". 
Is7ii 
ls77 
ls7s 
Is7'.l 

|SM) 

Is^l 

1 ^^■J 
lss:{ 
Isvl 
iss.-, 

ISMi 

ls^7 
isss 
Isyi 

IS'.M) 

lytl 

IS'.IJ 

l,v.i:( 
ivtt 
is;*:. 

iMKi 

lVi7 
iv's 
I Sim 

111! Ill 

mill 

I'.lDJ 
lIKCi 

I'llll 
I'll I.") 
i'l I) 
I'Ki; 

I III Is 

1'. II II I 

l!l|(l 
liUI 



I'U'iln'rTli»N ilK 

I'.iTATt'K-* IN 

'lHorrtANI>S OK 

BfnHELl* 



li)7,-J(tl 
',17, 7s:) 
loi;,i)'.)i) 
i:i:!,sst') 
ii;,77.'i 
ijii. t .J 
n :',,,", lii 
lori,(is'.» 
1(1,",, lis! 
Iiir>,s77 
l-'t,sJ7 

17(1,1 )',!-' 

i.M,r.'" 
iM,; , 

lil7.tiC>() 
ll»!l,l 1.") 
17il,'.i7:) 
L'lls.lCI 
HMI.IilJ 

17."),(tJ'.i 
lUs.d.M 
liil.lOH 
■Ji)-J,:!il-") 
■Jlll,ss! 
1 IS.JIM) 
■.',Vl,l-Jt 
1. ")(>,().")."■) 
ls:i,():it 
170,7.s7 
.".i",.-.':!7 



:.i-',; 



I.) 



iiu,i'ir> 
lir.',:int) 
2js,7s:! 
.M(),',t27 
1S7..V,IS 
•Jsi.tilU 
•J 17. lis 
:i:vj.s:<i) 
■J ii 1,7 11 

oOS.OHS 

.",ls,-_'li2 
•J7s,!ts,-) 
ii7t'>,.');t7 
:il',t.ii:i2 
2'.i-.>,7;?7 



.\v t.it Mil; 
F'\n\i Pun v; 
I'l It Hi >H1,I 
I'EIEMUKH 1. 

I.N Ce-nts 

■17 :! 

tM.'.t 
,■)'.»..•} 

•2 !t 
r>.-) (I 
.".:{ It 
.■>:{ , .'. 
(■..■) 2 
(il..") 
:ii 4 

(11. !t 

■i:} . 7 

,"),s . 7 
4;5 . () 

4S.;5 
01.0 
.-).-) 7 
42.2 

:ii».t) 

44 7 

■to , 7 
CiS 2 

10 2 
:i,-, . 4 
77). S 

;i.-).s 

t'li'i I 

.v.» 1 

,"i:i (1 

2i'i Ii 

2 s 1^ 

.-,1 7 

11 ) 
:('! 
1.1 1 
Vii 7 
17 I 
I'll 1 
|."i :; 
111 7 
.'il I 
r.l s 
7(1 11 

.'.I '.t 

7'.!.',) 



rKHCEN'T.KOF 
( IHV iK IS 
I'KOUl'fTItlN 



- .s 7i) 
+ .s,.".() 
+20. 20 

— 14.27 
+ 4.!r) 

— •") 77 

— Il .-il 

— 10 
■f-")7.40 
—2."). 20 
+:50.20 
—27.02 
+4(j.;52 

— 7.0<> 
— :U (to 
+.-|0,0.') 
+21 75 

- .s .12 

- ,s 10 

- :< 00 
— 2(1 20 
-i-.")0 00 
+ 1 2t 
—27.02 
+71.r.7 
-:<s 4:i 
+ lti s4 

(1 r.o 

• 71 111 
i.-> 1 1 
:it 07 

rl7 2.""i 

f IS 07 

- 7 s(l 

II III. 

• ."il 7'-' 
I;; is 

-;;i i,> 
'-M r.ii 

■ Is I t 

:; 17 

- (1 111 

-:il 07 

- 7,;;o 

1(1. l:i 



PERrENT.\«E 

C'h.\noe I.N 

I'BICE 



+:«):« 
-10.02 
-27.00 
.■)2 
OS 
74 
s7 



+.')! 
— 17 

r2l 



- .).(i7 
—44.07 
+ 70 04 



—'20 , 



+ 10. 


7.H 


+ SS 


41 


:is 


70 


-24 


24 


— 


10 


+ 12 


ss 


+ 4 


47 


+ 1(1 


04 


-41 


(to 


-11 


04 


+ 114 


12 


-52 


t i 


+ S4 


01 


-10 


14 


-50 


:i7 


+ 7 


52 


-01 


20 


24 


:il 


- O 


so 


f 10 


51 


+ 77 


00 


-:is 


50 



-HO :i(i 
•JO n 



■ :iil 

17 

• '.'O 

f 14 

■!•> 
-"I 



21 1 
Is 
04 
21 
21 
111 
15 



7 



(11 WTVM V 



Till. Mi;( iiAM>M ttr ( V(i.i;s 



■■ALMiriiltiii-c i- till' I'(iiiii(hili(iii 111' Maiiufartiiic :iiiil ('ciiiiiicrrf." 
—Mnlto of Ihc I'liiltd .^l(iU:< I)i i^drlinitit nf Agi [culture. 

Till s far in our iiivoti^atinu of the ra\\>v and law (it 
(■(•(iiKiiuic cycles, we ha\c sliown that the animal raintall 
in the iirincijial firain-prdducinfi ari'a nf the I nited 
States i)asses thniUfih (U^iinitc, v.ell-delined cycles; and 
tnat the yield of typical, leadinji cnip- is so clox'ly 
related to the rainfall of their respective critical seasons 
that the cyclical mo\-enient of the rainfall of the crilical 
seasons is aiM'i'oximately r. pritduced in the yield per 
aiTc of the correspondiiiii crop-- 'i'hese cycles ot crops 
constitute the natural, material current which dra^s 
upon its >iirfacc the la^jiiiiii'. rhythmically chan^iiiK 
values and iirice- with, which the economist is mdre 
immediately concerned. In order to understand the 
(•(innection l)etw(-en the How of the undercurrent ot 
aiii'icultural yield and tlie surface clian.iie^ of value> and 
price-, we ha\(' taken tlie nec(>>-ary lir>t stej) of con- 
necting the i)i'ice- of atiricultural commodities with 
their sujijily. l^ut tlie -iii)pl\- varies with the acreage as 
well as with the yi(>ld. an<l conscciuently to carr>- further 
nur inve-ti.iiatioii we mu>t know how closely the prices 
of crop> are related to their yield. 

93 



94 



Ennioniir Ci/rlcs: Their Ijnr aiid ('(tnsc 



Tin I'nCis (if Afirindliinil ('oiiinioditus Corrdnkd vdh 
Ihc Yiild of IIk' S(nr(d ('rnps 

The method (-iiploycd in the preceding ehaptor to 
derive llie law (if demand cf the several crops contained 
two stages: As a first stage, the correlation l)(>tween the 
relative change in th(> total supply and the corn>si)ond- 
ing relative change in price was assmned to he linear, 
and npon the liypothesis of linearity of regression, the 
demand curNc was computed and the degree of accuracy 
with which pric(-s might lie predicted from such linear 
demand curves we sliowcd how to m(-as>n-e. The second 
stage in the theoiy of demand curves was to assume a 
skew relation lietw(<Mi relative changes in pri( e and 
supi)ly, and we found that the degree of acciu-acy with 
whicli prices might he predicted from the sk(>w demand 
curves was greater than when the law of demand was 
assumed to he linear. We >hall follow these tw(t stages 
in treating lh(> relation hetweeii the yield per acre and 
the price of the crops. 

If the correlation l.etween the relative chang(> in 
yield i)er acre and the relative change in price is as- 
sumed to 1)0 lineal-, we olitain for the coefficients of 
correlation in case of 'he tour tyjiical crops, the values 
placed in th(> first row of the accompanying Tahlo, 
which, for iiurjiose of comiiarison. also presenf.s the 
corresponding coeiiicients in case of the linear demand 
cur\ ('^ . 



The Mi'chani.^m o/ Ti/c/cs 



'.».') 



A COMHAIUSON OF TIIK CoKKKUlKNTS (.K ( 'oKUKLATK "N 1 N 

Cask ok I.inkai: Vikld-I'uhk Ci kvks and ok I.inkak 

DkMAND (lliVKS 

^ ll Corn I Hay Cats I'olatdc' 



Relative chaiipc in ! 

yiel.l per acre an.l _ j^,; y.^ji i ._.7i8 

relative chaniie in I 

1 pritT ^i 



— .^7;{ 



Relative' change in'j 
total stii)i)ly anil ' -^^^ 
relative change in 
price l| 



71o ' —.722 



— 85() 



Tlie (lata used in tho abovo eotnputation were, in 
(•as(> of the yipld-i)rieo curve, tho average yield i)er acre 
of tlio respect iv" croiis in the whole of tho United 
States and the eorresi)ondinf; averajjo prices for tho 
United States, on the first of December of tho years in 
which tho crops were produced. The data for the 
demand curves, it will be recalled fr.m tho pr.M'ediiif? 
chapter, were the total sui)i)ly of the resiiective croi)s 
in the United States and tho correspimduis prices on 
December 1. The i)eri(Hi covered in l)otli cases was 
from ISdt) to 1911, inclusively. The data were ob- 
tained from rec{>nt Yfarbooks of the I'nited States 
Department of AM;rictilture. 

It ai)p(>:!'-s, from tho coefficients of correlation pivon 
in the above Table, that it is p()ssii)le to iiredict tho 
pric(>s of the crops from the yield per aero with tho same 



•It.) i'.nniitiiiir Ci/chs: 'I'luir l.iiir tind ('aiisi 

procisidii with which in'icfs iii;iy lie iircdictcd I'roin tho 
(loiiKUid (Mir\('-. Or, t" imt the idea in aimihci- t'onn, 
the i)|-o(hicti\ ity of thr -nil i- a- rln^dy I'datcd to tlic 
prices of crop- a- t he -ui)ply of the comiiiodily i> related 
to the -aine pi'ice-. Ill tlie <'haiitei' on the "Law of 
I)eiiiaii(L" we found that, wlien the relati\c chaii^ic in 
tlie >ni)ply is jiivcn. tiie mean -hift in the coriT-poniHnm 
clianjie of i)fice may lie chtained frnm tlie rejifcssiou 
(■(Illation, and that, fuithennofe, the root-m(>an-s(iuare 
deviation of the ohscrMitioiis may he coniputcd hy 



the formula N = cr,,^ 1 -r'-. 1 his same tormuia may 
lie used for a similar puipose in case of the yield-price 
curves. 

We come now to the s(-cond stage in the derivation of 
the relation between i)rice and die yield i)er acre ot 
crojjs. We a— ume tliat the relation hetwecn tlie yield 
per acre .md tlie price of a croj) is skew, and that tho 
relation lielweeii the two may he expre.-sed 1)\- an 
ei (nation of the form // =" -H''-r+('.r ' + '/.r\ 

in I'imire L'i, the skew yield-jirice ciir\-es of our four 
|-epresentati\(' commodities are drawn to a iterceiitagc 
-cale, 'I'lie ('(Illations to the cuiacs. which were com- 
pute(| hy the Method of I.ea-t Si iiiares, a I'e i:i\-en upon 
the I'iiiure. The i-oot-mean-s(|uare (le\iation ot tli(^ 
oh-ervation- from their rc-pecti\(' yield-price curves 
are '^\\v\i in the following' I'ahli^ which, lor i)uri)os(>s 
of coniiiari-oii. rei)roduce- the coetlicients that uer(^ 
lound, in the i)iecedinu: chapter, to measure the devia- 
tion of thi- oh-cr\atio:,- aJioiiI the -kew laws nf d(-- 
m.and. 



The Mtrhani.sin of Cijrli 



97 




Av../,V ^"-^ '" "'y''''^" ''''''"'" "''"'"^" ''""^' '" '"''""^" ""■ '"''""'" 

l.-,„,KK 21^ Thr .vl:..,..,, lH..u,.,.n thr pri.v an.l fh. yi.l-i P-r am- of the 

several cTnp-.. 
Wh.ii tlieoiiLnii w at ('», Wi. the .•<iuati(ms are 

h.rcnrii ./ - IT - 1 •J'tSllr + .(tlS'.fJ.f^ -.<M)()i;i7.r'. 
l..„.hav V = 1.17 -l(lJl.V + .01.-,4<../= + .tH)00!t.r\ 

For potatoes, ;/ = -Ml - 1 l^tM..- t- .(U-MK!.,= 



(HMU 11j\ 



98 Economic Cijrlis: Tin ir Lmc mid Come 

A ( 'iiMi'.\KiM)\ OK riiK l{i)nr-.Mi.\N-Si^( \K!; I)i;\i\iii>\ i\ 
('\>i; OK Skkw ViKLD-l'uiu, ('tini.^ \.M) oi Ski.w Di- 
M \\u ( 'rii\ i;s 







-^ 


icld-Prid- 
( 'iirvcs 




T")('nia!iil 
( 'urvcs 



Corn 



5.48 



Hay 



5.72 



7.36 



4.65 



Oats 



Pot at Off 



o.j •( :v.i 



10.17 



1> (U 



I''roiu the results gixcii in the last two Tallies, it i> clear 
that the prices of the representative crops are as closely 
related to the yield per acre as to the total supply of the 
crops. This conclusion is of importance in the task of 
connect insi; the cycles in th(> productivity of the soil with 
the cycles in values and prices. 

In ohtaiiiiii}!! the ])recodinK clost> relations l)(>t\ve(>n the 
cliaiifies in ])rices and changes in yield, the figures for tiie 
whole of the I'nited States wei-e employed. The oiiject 
of liroadeniiij!; th(> tielil of observation from the detailed 
investitiation of the Middle West to the whole of the 
I'liited States wa> two-fold; I'irst , it seemed likely, r; 
priori, that a more intimate relation between prices and 
yield woidd li(> obtained if the larjie market of the \vhol(> 
country were substituted for the local market of Illinois; 
secondly, because ^he object of this chapter is to briiifz; 
the ])hysical cycl(>s of crops into relation with the 
iiidust rial and comm<>rcial chan^i's of the whol(> country, 
and to this end it seemed desii-al>le that the crojjs of the 



The Mcchnnisni of Citrlcfi 



!)<) 



wholo country sIk.uI.I l.c ('..nsidcivd. WV iic<'<l, how- 
ever, to assure ourselves tl.at. ii taking tliis more 
(•onipreheiisiv(> ' 'W of tlie yieU of crops, we have not 
lost \hr chara<'teristic cyclical luoveinent of the yield 
which we discovered in the more limited studv. We 
desire to know how closely th.> yield per acre of the 
whole country is correlated with tiie yield i)er acre of 
our r 'xresentutive state of Illinois. 

The correlations of the annual ditTerences in the yield 
per acre in Illinois and the aiuuial ditTerences in the 
yield per acre in the I'nited States were, in case of our 
four typical crops, for corn, r = .S.")r); for hay. r = .7-ir,; 
for oats, r = .SOO; for potatoes, r = .S4:}. The period 
covered in all cases was from iSCli to VMI inclusively. 
The data were obtained from Hulhiins. :>(). .')S, (12, (vi 
of the Buroaii o^ Statistics of the United States Deparl- 
inent of Agricultur(> and from the rec(>nt Ymrhoohs of 
the same Department. .\ reference to the Tal.le fiiven 

a moment ago ^vill ^1>"W 'l>;i< '»'<' >'*'l*l '"''' ''''''' "^ ''''"'''' 
in Illinois is at least as closely r(«lated to the yi<>ld per 
acre of the same crons in tlie Tnited Stat.'s, as the prices 
of the several croiis are related either to the supply 
of the crops or to the yield i.er acre of the crops. More- 
over, the very high values of the co(>f!icients l.>ave but 
little room for doubt that the cyclical movement of the 
yield per acr.^ in the Middle West is representative of 
the movement of the cn.p yield in the whole of the 
United States. 



100 r.i'Diiiiiiiic Ci/clis: 'I'Ik ir Lair and ('<iiisr 



R'simi (111(1 FitUiiKi I'l-irra ns h'llatnl to )' i< hl-l'nrc 

( ' urr, ■•< 

Tluis l:ir it i> clcjir that the |)n'(licti(tn i>f agricul- 
tural jiriccs is (Icpciidriit rpoii a Uuowlcdtic (1) of the 
law dl' tlic \aiiati()iis di" i)ri('c with the yiclil per ai'r(\ 
ami C-'i nf tlic law lit' the annual rliaimc in the yield per 
acri- nf the >c\(M-ai vvn\)>. If the iclation lu'twccn prircs 
and yield per acre were cdnstanl, the theory .)f agricul- 
tural cycles would he conipl''tely elucidated; for, once 
having discovered the law of the relation of price to 
yield pei- acie, nothing more would he neces-ary then 
to connect the yield with the meteorological conditions 
of its critical season, and the resulting nrices for a lon^ 
term of years could he predicted with jireat |)rohahility. 
But the relation hetween th(> price of the crops and the 
yield per acre varies with the I(>vel of general prices, and 
it is of the first importance to know the manner of varia- 
tion. 

If the course of pric(>s in the I'nited States for the 
period iShti to I'.tll is examined, it will he seen that, 
in p'lieral terms, we m.ay with justness characterize tlH> 
period ISdii to IS'.lilasa period of fallinji prices, and the 
pcM-iod 1S'.)() to i'.tll as a period of risiuff jirices. If 
therefore, in case of (>ach of our rei)resentali\-e com- 
modities, we construct twii yield-pi'ice curves, one 
for th(> period of fallinji i)rices and one for the pe- 
riod of i'i>ing prices, we shall, l»y comitarinji the two 
curves for the two periods, discover how the demand 
curves, or yield-jjrice eur\c-. vary ii. periods in which 



'/■//( MdhiinisHi (i) ('jichs 



101 



tlu- in..v.'tnrnt .-f ^.MM■^lll |)n''<"> i- •" "ppoMtc .liivr- 

Ill iMiiuiv 'J'J. ilic '■iiili' 'urvc- lire ilrawti. ( ■(.iiii>ai-- 
iiiK the curvo in llu' tw.. p.Tin.l- lnr vavU --f tlu' l'"ur 
rcprcsi'iitat'p-.' rvnp^ we iiit<'i lliat 

i 1 , tlu- .l.Muaiul x'li.'.lulc ,.r yi>'l.l-i>n<v :airv.' i^ liinh 
wh.u tlu' fi.'ii.Tal l.'vcl (.1 |>ric.-s is hitrli: i'IkI 
,1„, ,l(Mnan.l ^cli.'dul. i> low when the trcncral 
level (if prices is low: 

(2) \ho jrcncral run of tli»" riirvc- rcniaiiis nearly the 
same. That i> to say, the princil)al ditiereiice 
hctwecMi th(> period of falling: pri.rs ami period 
of risinsi i)rice^ is that the yield-l)rico schedules 
move down or up. 

These are general statements in which (piite obvious 
d.wiations are ignored and whi.'h. conse-iuently. do 
not pretend to (piaiititative accuracy. The construc- 
tion of the ciu-ves is depemleut upon too few observa- 
tions to admit of attaching signilicauce to tlie ai)parent 
oxceptions to the rule. 

Since the prices of th(> re|)r<'seutative crops are, as we 
know, .hM-endent ui)on tlu> yiel.l i.er acre and the law 
,)f the relation l)etween |)ri.'es and the yield per a<-re, 
and since, as we have proved, the yield-price curves 
move with the general level of i)rices, our desideratum 
is to discover what determines the change in the level 
of general prices. 



1{»2 



/•; 



:ciiniiiini' 



( ' iirli s: 'I'lnir Loir mnl (diisr 



I.. 

1 

K 
t 



^ 



i 



C „ 







i 

r 






Pf.(f„fg^f chsn^r " thrf.rld perncre ^'f'.M's ^nfnts^r chan^einthtfifldperarreaf^poldtvet 



V. ■_'.' Till- irlaiiiiii hrlvvccn the ;>rici' 

M vrral (Ti'ii 
llic nriL'iri IS lit ('),"i, tlic ciiuatiDiis arc 

"'" ■ yrs. IVMV I'.Ml, - . // = ii'Hi 

yrs. Istiti-lSS'.), 

yrs. 1><!H> 1(111, 

yrs. I'^i'iii I^Vt, 

yrs. IVXf I'.Ul, 

' vrs. IStiti INSO, 
I'lir iKitatiirs \ ■ 



III tli( 



(1 per 



W 



I'lir h.'iv 



lor nul- 



1 (I'J'.l'.t.r r 01'.IJlu- = 

l,ls'.lt.r t .017:f7.r' 

ItVlii.V ^.I>77'.)^J■■' 

-■.im.r IKI.'j'.ll./' 



.f (he 



lMM):il_V\ 
Omdll'tr'. 
.(HKI.',71j-' 
.(H)(M)7."),r' 



yrs. l^'.ll) I'M 1. 



"),tl - 

>-S --l.f,0:ii.tx -.(H).'>lli.r2 f-.(HM>77S.r'. 

.!»<)- 1.024()J- f .()_';i()l/' -.(XHUVi.r-'. 

;/ = — H.ifJ— 1.4424j + .OltJ.S4j-»-.()(HH).;().ri. 

/y = — .'Jl -l.f>0<'.S.r+ (i:Kil.r» -,(HM):}',I7j->. 



TIh Mil liilinslii III ('ncl' ■ 



103 



Til. Vi.hni ■,-n.,.ni..ni.i .Wlmli, oil uil.slri, 

W.. <lK,ll MPl-u:,,-!, ,1,.. ,.n.l.l..n..MlHT:M.-— 'I"- 

nn.lur.T^- N ^^l-- tlur, um-hm. :hv .rnrraly n- 

,.„.,l..,l.-,..,l,..~nM!,..:u.nvHv.M.:M,.-.' ^2. l^.h. 
,,. „,.l.n,:,n.llnr , •.„,., l.-.vp,.nll:,w ,lK,l i-nrr- 



liii-fil in I 



1„. .l..„K,ii.l 1-rall ronnuM.lUH.^, nr w .« not 
,,UlH.r -luT... .1.:,- -h.bu „!■ W.nKUnMor pun. ,.ru. 

,,„,„„„, ,„,,hoM.n„nn,..n.H-.,iul.H.hnurlourrn,,.^ 



;irc -ain|>lt'- 



,. ,li;ill rdll-hll'l' in a 
■;ir \lpiill tll( 



,„,nMno,l,lH.l.nl,nn..l^M.,ntn-anr..lolH.:,rup.n.lH. 

,,.Milt-tl,a. l:aNral.va,lylM...M'MaM.~lH'W 

„,■,,„,„. an... wmMlH..x..'n.nnln.a.-n.a,.a,HluMl: 

,1... av.Ta... vH.ia PM' a,av TIh. MU.^Un,, „1 .ntnvM 
„.„,„,!,..,.,„„. ,~ulH-lHM-.lH.Nolnnu.n,pnHlun.r> 

p.nd- Ihiclualt 



.. with llir virM |>n- anv nl ih.' cn.p. 



\\V ^l.alln.vrM^al. llu-.,U.Mion,an.l.a-a niran- nt 

,,,,v.u.. iorwanl nur ,n,,un-y w. luM r-n^trurt an 
„„l,^xnun,lu.ro,-,lu.v,.Mp.rar,vof.nM- 'l !..■ nu,. 
,,„,,,, „,lu.rnn.u S,aH.^wl,n..vH.M ,.Ta,avthrnu., - 

„„ , ,,„., ,,..,.,,..1 ,~ .vr„nl,.a u. .In. V,.r/ /,snt ,1„. 

,,„,,^,,,,„,„ ,.,A.nrul.inva,v:rorn.wh..at.,>at^,l.a>- 
,„v ,v,..lu.rkwlH-a>,polaP.r^.hay.o,tP>n/ U.u^r... 



104 Kntiiiiinir Cifclrs: Thi ir l.'iir (iml Citiisc 

,,t r.irli <'\ lll.M' r|ii|i-, llir llir;ill \ IrM Jifr ;irrr |i.r tho 

ypnrs IS'lil IMi't i- i.ikin .1^ a ha-c and llu' viiil per 

an-c fell- I'a.li Ml' ilir year- I^Tn I'M I i- r\|)rr--((l a- a 

nilK, (,!' ihr liaM'. ci.iiiparalili' iikIhi- l^r' the ci-np- dur- 

iiili Ilic priidd lit' lnM>-t\\ii >car> will I"' iililaiiu'd. in 

ordiT III niliiiillic llic lillir -cric^ nl' llUUfc^ illtii a >cru's 

tliat -liall lit' i( invM'iilatiM' nt' llu' wlml"' "t atiriciilt iin'. 

thr -.'MTal -iTii- iiiu-'l 111' pn>iifiiy wcii^hlcd. 'I'lic 

liii'lhnd lit' urinliijim ihal w a - adiijilcd in ihi- particular 

ca-c Vka- til a--iuii tn rarli crnp au iiiiiinilaiicc pmixir- 

ticliatc til It- \alui' a~ riiinpaicd uitli liir tntal \alut' <>( 

th(> iiiiii' cpiii- in I'.tll. d'h" -rsrial \vciiilit> wciv: fur 

ciirn. :')•'); whral. 12; nat-, '.•; liaiii'X'. :<: rye, .7; \nuk- 

wlical, .;{; piitatni-., (■»; lia\ , 1*1; nittnn. 17. d'lif index 

iiiiiiil.ri- arc iii\cn in TaMi' I nt' thr Ap|)<Midi\ to tlii-; 

cliaptcr. 

P.ct'iirr cimipariim tlic index niinilicr for the yicM 
jicr acre nl' the crnp- with tlic Miluinc nt' iinnluccrs 
^ihkU. \\c iiiu-t make -lire that we are keeping; idnse 
t,, tlir iv-iilt- nlitained Inmi a detaile(l inve-t itiatioii 
ut' niir t'liiir repi'e-eiitatue crnp-. ll' ail index nunilier ot 
the t'niir repre-eiitalive cmii- is cnn^t riicteil uimn the 
same principle a- the index t'nr th<' nine ernp<, Imw 
cin-eh wmild the iiidice- he cnrrelated'.' In eninpul iiifl 
the index nt' till' yield per acre nt' the t'niir rei)resenta- 
ti\c crnp-. the weight.- a — itiiied were: t'nr cnrn, ")(); 
iiuv, 2S; nats. lo; pntatn-,-. 7. d'he index is ^^ivcii in 



1;iitic<l fniiu firciiUir ;iL', Kurciii el' Slatwics, \' . .■^. I )ip:iitrii(iit ef 
A>xrir\ilturc. The yicM fur lull was (ilitaiinil lieni ilic Yxulxnil: 
of llir Di'partniciii i.t' .Xiiiiniii inv. i'Ml. 



Th, Miilmiiism iij ('nclis 



105 



.|-,i,,, 1 ,,,• ,1,.. Air-iHl'^ '" ""^ '•''^"'"■'' ■'"'"' ' "'" 

,„,„t nl- rnnvlulum l-tu.'M. t!,. umI.x Inr >!i<- f">'r 
,,,.,..r„.:,..v,...rn,.:,n,l ,!,.. .n-l.x f-r t hr .,.,.,■ .T.-ps, 

is r .M'Wt. 

1, is a .•..i,m...n ul.-m almii ,.t wnt.T-. nu .•.■ui.on.i.-. 
,nM.. thai tl„. pro.lu.ti-.r, uf lui-in... i^ an un.KUally 

J. 1 l.arunu.t.r -f tnuk. TIh a,n..uHt nf pi^^-.n.n 

that is a..n,>allv prn,lur,.,l ^«. -i- with th. arfvity 
an.lvuh.n.rMfn.hi-trva.Hltra.lr, an.l.t ,. an....U th.< 
li,.., n.n.uMMhlu- tu MMlirat.. thr tirnrral shru.ki.ili .n 
,hr ultiuKlt,. .Ir.na.Hl uh.rh chrrks tl,r artivUv nt 
,,,,!.• a.ul ra.x.- ,t . trn.P'.fary 'I'-li"-- 1^ "'"•'■'• ^'''^ 
,,,,,„„„. lu'tuvrn Ih. n.ov..M,rnt uf this l.aru.n.'trr nt 

,,a.lr, thr P<'"1"'''""' "'■'"«-■"•""••""' ''"•'•>-''l''^"f '1"^ 
,.,„,,.■• Can it iK'that tl,r iu.TraM' a.nl .l.M'.-aM. cf th.- 
••ulti.uatr ,i.n,:.i,.r' ^^hu■h !,(< hark nf thr tlnvv an.l 
,,1,1, .,f IraM.. ha> it> m-uit- in thr .•ydi.'al uinvciiu'iits 
,,f the vi.'M per acre nf thr cn-ps'.' 

'[■lie data fnr t(-lin- uhrth.T thriv i^ a ivlatici. 1..- 
tuvn the virKl |ht aciv oi thr rrul- and tl,.- .-.nnual 
,„,„l,„,i,muf piir-irnn an. ih.-tal istir< ..f th.' annual 
,„,„lu,,ion of pi-inm a.ul th- .lulcx nun;lMTS ..f iho 
yield piT acre xi "iir nine crops. 

T\w MU'thod of icslin},' the relation |.rr>ents diliicnl- 
ti,-. and as it will he .iscd a^iain to n.eaMUV the relation 
hHween th.' eyele> of er,.p> an.l the .•ycl.-s of fi.-neral 
pri.'.'s, we shall have a tirni.'r p-aS' up"" ""r problem 
if w.-st..p now t.. Kain a el.'ar ulea ..f th.' frnis tha,, 
eontiiuially o.aair in th<- ar^uuu'Ut. In any one ..1 the 



KKi F.ci>ni>inif Ci/rlrs: 'llicir Ijiic mnl <'<ni!<( 



scries of limuivs that we shall use there are three distinct 
iiidveiiu'iits which need to lie discriiiiitKiti'ti, and when 
any two of the scries are coniparci', anotlier important 
cliaracteristic of tlie >cries re(iuiies to lie taken into 
account. The three niox'einenis that are comliined in 
eac'ii series are; 

tn) Ttie continuons fall or rise of the li<:nres with the 
How of time. 'I'his mo\cmetit will he referred 
to a- tlie >ecular trend of the ti^nres; 
(b) The rhythmical ihiciuatioii of tlie liiiures alioni 
their -eeiilar trend. When thi> movement 
snperpox-d upon the -ecular trend i- the oh- 
j(>ct of invest iiiati" III. the coniliiueil niovenient 
will lie referred '.i as tli(> <i(>neral cyclical 
inovnieiit of the lijiures. \\1umi the rhyth- 
mical nio\-ement unaffected hy the complieat- 
iiifi trend is lieinjii; considered, it will he referreil 
to simply as the cycles of the tiiiure-: 
(c~i The year to year temporary tluctuatmn ahout 
the jicneral cyclical moxcmi lit . The-e tluciua- 
tion> will lie ivferred to a- the deviations of 
the r;tiure>. 
When t'le cycle- of any Ino -erics are eompared. it will 
friMiueiitly happen, pai't icnlarly if the one series is the 
cause of the other, that there is a con>ideialile interval 
hetweeti t!ie corre-poiidini!; pcrts of the cycles in the 
two series. Thi- interv.al will he referred lo a- the laii 
of the second -eiies. 

We shall he intere-!ed throuLihout the re-t oi this 
chajiter iirimaril\ in the interrelations of cycles oi 



77 ■ Michanisin aj Clicks 107 

ernp< cv.'l.'s in the activily oi i.ulustiy. an.l cyrlr. in 
..Mirrarprirrs. I'.ut Nvr appn.u'h uur geurral ,>rol.l...u 
l,v nm^uUM-in^ ln-<t ,1,. trnipnrary llu.^tuatums wl.irh 

^;,. iK.vo a,.v...l to call .Irv.atious. and u. .u-iuire 
.vhrtluT thrrn is a n.lat.nu lu.tw...u tlH- drv.at.ous of 

,h, viria of thr crnps and llHMl..vialinns in thepHHluc- 



'.)'. 



,„,, .,f ,„,,„.. •.h.nu.hodthatuasa.lopt.a.as 
,.,., ,o obtain tlu> iienrral cyrliral n.-v.-nicnts ot tho 
,,„ ,,,,i,.s l.y av..r:„in^. in .'as,- of ..a..)! mths, th. 
t,„un-. for oach yoar w,th tlu> titi.nvs that nnnH.a.at..ly 

p;...,.a..d an.l follow...! thr^i'..uyoar. F.,r oxan.pUs 
,,,i,a..xnuna>..r..ftlH->i..iap..ru<.vf..rtlu.y-rs 
,s7,. is71,lS72.1S7;Mv...viv^p..'tiv..lyl()S, 1.).., no. 
.,ll,tiuivf.>rtli.>>i<'l<l !>'■!• acre m is, 1 

10S+ UjM-no ^:v_';5 ^j^j_.._ j^;,,^i. 

woul.l th.T.'fon' 1)1' - 2 ;5 

,,,K. ,„...,nooth...lin.l.>xf..rlS7•_>^voulal)..l<)^.7. In 
T,l.l,.^ 11 an.llll .)f th.' Ai)p..n.r.x to this chapt.-r ar.. 
,,.,..nt...l the ..a.inal an.l th.> sn,...„h...l figures lor th.. 
,,-...lu..t>.,n..fpi.-in.nan.lfortluMn.l,.xmnnlKT<.tth.. 

;.,..Mp..ra..n..,fth..nnu-.-n.ps. Tlu' stat.stu.s o h.. 
pn.hu.t.on ..f p..-m.n w..,v ohtain.^.l tn.n lho_N.,/..- 
^.„^,, ,,..,,„,, of ,h.-rni..-aSlat.>sf..rl'.U2, p. n4. 
' \f„.,.th.....n..ral..y.'li.'aln>..v.nn...ls..fth.Mw.>s.a-H.s 

,.;,... .l,.,..nnnu..l, ,h.- .l.'VUUu-ns ..i tl. a.-tual h.u.vs 

,,,„ „. .n.u.,h...l t„u,vs for ..a..h .)f tlu- years ...v 

..al..nlat..lh,.-hoth..n..s.,fh.u...>. ■'■;-;<•----;; 
,,.,,l.o^;v..>u.Tahl..s liana 111 olth."App.'n.hx to 



!"•' 



"lis chapt.T. Thr .iu..>ti..! 



I „uon which tlu->." aifi'c'-- 



ci 



,,es a.v 1.. throw U^ht may UMUit nMhist..nn: 



Is 



lOS I'ciiiioinif ('iidix: Their Ijiir mifl Ciiusr 

t\v Icviatidii of tlic yicli! per acre of the crnps from its 
ficiicral cyclical ino\-ciiiciit a>sociatc(l with the devia- 
tion, in the followiiifi year, of the i)io(luction of i)i«- 
iron from the licneral cyclical movement of piti-iion'.' 
The answer is found I'y correlating the diffei'cnces. 
always rememliei-iiiK that the dit'feirnce for the \ield 
j)er acre in any jiiven year is to he taken with the dif- 
ference of the iiroduclion of jiifi iron in the followini!; 
year. Tlu coefricient of cori'el.ation is r .'Jol. 



A\'e come now to the association hd^ e(>n the cyclical 
nio\-ement of the yield per acre of ii.e ci'ops and the 
eyclical moNcment of the pi'oduction of pi^-iron. I'.ach 
of lhe>e movement,- is Miju'i-posed uiion a ri>inu secular 
trend, and before we can tot tlie dejiive in which the 
cycles are ivlated the >ecular t rend< must he eliminated. 
If, as a hrst approximation, the seculai' trend in each 
case is a.-Mimed to he linear, then hy littin^ a straight 
line ' to the data, it i.- iios>iiile to calculate the lluctua- 
tions of the cycles of ci-oj) yield ami of ])roduction of 
piji-iron ahout their re-pective trends, and tliese iluct na- 
tions may Ix' corivlated. In 'hahle 1\' of the Apjx'ndix 
to this chai)ter. the data lor the c;ilculation of the con- 
nection Iie1w(>en the cycle> are ^ii\-en. In columns 2 
and .") are tah\ilated the p:enei'al cyclical mo\cmen1s (A 

'The c(iii:it'niM to the liiirMV ^' cuhir iniids arc, ns] cclivi ly, 
i/ = .IM4j+it.^..')7.fi.r the yicM l cr ;u'ic(,f ere] ,-;; and ii = ')S2.7\j- + 
9.")2,'). fcr the i-rcduclicn cf i.if;-iniii. 'I'lic (.tiy.in in tLc firsi cn.M' is 
!it ls71 and in till latti r i"i.~c, at IV.'d. Tlir (iiM i ipiatii n \\a> r( iii- 
putcd from the <lata fnr t!ic years Is71 llidC. and tlic ■cciiid .(illa- 
tion, from the dalu for 1S71 to HMO. 



The Mccli(Uii-<m of ( './/r^ s 



109 



„,.. VH.I.I por aero of Ih. . •.-..,» au.l of tluMH-aurtKm uf 

p,.i,,.u; i.i .■..lu.nns r. and .i. tlu. values of ,1,. hnrar 
sm.lartn.mlsa.vpv..n;a.ulmn.lu>nns4au.l . . t u- 

deviati.ms nf tb- .•yrli.al u.ovrnH.nt fmn, tlu- ..-•ular 
,,,,,lar.>n'n.nl.Hl. TIth. last. l..viatiun< ar. llu. n.a- 

„,,ial fur ralrulaliuu; the rouurr.inu l^'twrru llu' cycU's 
.,f ,U. yu'l.l ,u.r urn- of th. .Tops au.l th. ryrl,.> ..1 tho 

nrochictinii of pifi-'n'oii. 

If ,he .Icviat.ons of tl.r ryrW f.-.a thrir rosp..ct.vo 

soc-ular tmi.ls an-rom.laP.a. th. rorfliriont of •■onrh- 
ti,„ n>a.'hos tho val.u-, r ^ .iV2n. but w. must not l.o 
,„„„„ to assuuH- tl,at rveu thi> rrlativ-ly h>,h ro- 
.,„i,,,„ ,,,p,v..uts thr full a.-pv.- of tlH> r.lat.on U>- 
,w..(Mi tlu> .•vliral niovc.nrut of the <Toi'< ^^'-l ''"^ 
evM .nov.uHMit of tiu- activity of m.lu^try as t^hat 
.".tivity is tv|nlu>a in tl.o production ot p.'-ron. It i> 
;.,a. likolv that tlH> ^oo.l or iKul .Tops n.ay pn-.luoo 
tlH-ir nutxinunn .^tl-.^t at a .■..nsi.l..raMc infrxal aft..- 
„^, ,,,,,,a in ^vln.■h the .•nM- ar.. a.^tually harv..^t.HL 
Ti,n.^ is r.Miui,r.l f..r th.> .■han^in^ pro.hu't.v.ty ..t 
,,op. t.. worl< ..ut its nmxnnun>..tT,H.t, ami tins .« 

,la,i,Uh.>a.iiustnHM.. ..fth.'.'yl'-"f'l-="'''^-''>'';^ 
industrv to th.. .•y.'U.s ..f tlu. yi.'Ul ..f tlH' .T-ps. Wo 

must WivvvUn-v nu-asuiv tlu' aui.uint of the la^. 

lfinst(-a.l .f....nrlatin^th.M.y..l,>softh.>yi.'i.l.'ftb.> 
orops an.l ..f tlu> pro.Uu'ti.m ..f l-i^-ir-m f..r corr.-spon.l- 
i„S years, w. .•..nvlat,. th.Mn for la^s of vari..us uit.n-vals 
we shall iin.l it p.>ssihl." t.. d..t..rnnn.> th.> la^ that will 
piv.. tho nuixiniuni .•o..frua..nt of .•..nvlatmn, an.l tins 

^^,-,,^^, vaUu> of the la, ^v.^ n,ay tlu-n n.^ard as the 



1 K) I'A-iiiiiittiir Ci/clis: Tin ir l.uir nml Cause 

iiitii'\;il 111' tunc icijiiircd for the cycle- ill the crdp- to 
pl-oillici' their iii;i\iliiUin clVect upon the cycle.- ot the 
acti\ity 111' iiidu-tiy. \\\u\i the c;i Icuhil ioii of tlie co- 
(■lllcieiii> of coiivhiiii.u i- iiiaile according to this plan, 
it IS foiiiul that for a la'j; 

or /I PI years, ;• = .(i'_'5; 

()l line \c:ir, r— .Till; 

Of lud years, r= .7 IS; 

( >t tliric years, r= .W~: 

Ol idiii' >i'ars. r — .'t~'2. 

It is cleai', therefoie, t! .\t the cycles in the yield l)er 
acre of the crops are iiit iiii;i!el\- related to the c'\'cles in 
the act i\ itv of iiidu-tiA- and that it takes hei ween one 
and two vears for \.' ir had crop- to i)ro(luci> th<' 

iiiaxiiiiuiii eiVect 111 I ,1 ''"' :i<'tivity of the pi'j:-iroii in- 
dii-trv. l-'isiiire '_':> illu-lraies th" «ieiie;'al coniiiuence 
of the c\ cles of th.e crops and of th(M'\ cles in the prodnc- 
tioii of iiiti-iroii when a iau; of tuo years is cliniiiiated. 

\s to ilie general ([iie-tion concerning; the I'daticn 
heiween the hafve-t- aiid the acti\ity of indu-try, we 
nia\- conclude from our -tati-tical iiKjuirv tliat there is 
a po>iti\e, Hiiiinate connection, and \-ery ])rol ably a 
direct cau-al relation, lieiweeii th(> lioiinty or niggardli- 
ness of nature and the How or el>l) of trade.' 

,1 Kciv Tjijii' ({f P( iinni'I Ciirrr 

A inoment ;iiro, we saw that two iireliniinary prohlems 

li;,d 1,1 he ti'eated hefoi-e we could Jia-s to the direct 

' III a later .-eetliili ul' tlie eliapler the liietliiiil that has been ll>(tl 
ill tieatiiif; thi- prohli'in will he ottiployed for another purimse and 
will iheti lie illiisn-ate.l in il. i.iil hy nieai.s i f uraphs. 



Till Mdliiiiii'^'" "J ' i^''^''-'* 



II 



<,e product.cn ofpfirvn fron, ,ti ,ecuhr r,,r,<i. 
'^ o 9 o 

§ 




^.,..i..^^>^.--^-'^--— ^'^^''^'"•"'^'"^"""'^ 



112 F.C()>i())tiif ('iirlis: I'lii ir fjiir (\tiil C(ia-<(' 



(•i)ii-i(lcr;ttii)n nf the (•.■lu-c .■iml law nf cycle-; (it general 
I)ric«>s. 'I'lic Uy>\ nl' thoc iircliininary pi-nlilcms. uanicly, 
the iiil'ui'licc (if the luilllitN nf liatUl'c Up"ili the VdllUili' 
and acti\ity nf ti-adc. \\c tiaxc 'ii>t (liscii>~(Ml, and wc 
collie ridw to the x'cond preliniiiiar>' jn'olilein, which 
we >liall imt in tlie form of a ([notion; Are all demand 
curves in a dynamic -ociety of the >ame tyix" as the 
demand curve.^ for the i-epre-entati\(' ci'ops: corn, hay, 
oats, and potatoes? 

'I'his (jnestion mu-t lie answered a- a pndiminary to 
the moi'c fnii(lamental iminiry as to the can>e ot cycles 
of ^enei'al prici'-, liecan-e if we a--ume that all demand 
ciu'vo are of the ^ame neu:ati\(' type, we are confronted 
with an imp<is>i!iility at the wvy heirinninu: of our iii- 
vesti^.ation. I'pon the a-^umiition that ;ill dem.and 
('ur\cs ar'e of the nefj;ati\(' type, it wonld lie imjiossilile 
for ^eiiei'al price- to fall while the yield per acre of 
crops is decreasing:, in conse(nienc(' of the 'lecrease 
in the yield jier acre, tlie piice of crops would ascend, 
tlie volume of commodities repi'i ented liy pi(i-iron 
would decrease, and upon the hypothesis of the uni- 
V(>rsality of the descendinji type of demand cui'ves, the 
prices of commodities like jiiii-iron would ri:-e. In a 
jieriod of declining yield of croiis, therefore, there v-'oiild 
he a I'ise of prices, and in a period of increasinji yield of 
crops there would lie a fall of prices. Piut the facts are 
exactly the contrary. During the lonji pi'riod of falling 
pricos from ls7(> to 1S',)0, there was a doorcase in the 
yield p(>r acre of the ci'ojjs, and durmu; the ion^; jieriod 
of ri-iuLi' price> from JSilll to Mill, there wa> an increas- 



The Mirhdi'isni nj Ci/rlrs 



113 



,.^,nnr tl.at lu :. .ly.ia.nic >nr>.-ty th-.v ,^ o,... laNV nt 
.l,.,Hana for all n.nnnu.l.tu.s. Tl.' .l.-^riua ui th. un.- 
f„,„„y ..f the law Mf a..nKUHri> uu i.lol of tl.r static 

"lt''tl.T(« aiv .litTr.vnc- in ty!H-> of .Ic.na.M rnrv.-s, 
i,is,iuit..l>krlythata^ou...y,H.ha.hr..nil'uMrat...ll>y 

the vvn\) 



.^,„,1„,, ,v,H. will 1m' .•x.Mui.lilM'.l I'.v pun- 
,,,„.lu,...r~ ^o,Kl>. WV shall acn.nlin,ly i.uvsti.at. 
„,,, .,,,„„„i ,,a.v.. ..I- in^-.n.u, .air ,vinvs..itat.vc pn- 

iku'cfs' u;.)ihI. 

lu Tal.l.- V ..1 th.- App.'u.lix \n this .•hapt.T )s ,.ou- 
fxiiUMl th.. .nat.T.al f.>r th- .•o.nputati.m .-f tlu- law ..f 
,,^,,„„,l un- ,.-^-n-<.n. Tl.' annual p..n...nta,.. .'han^-s 
in ,lu. pnuh..'li..n .>f pi^-inm w.t.. .•..n,pu..Ml (nun the 
ti.ures ..f annual pn.du..t>..n. whi.^li w.uv tak.'u In.ni 
t},,Statisl!adAhstrarl^nvm-2.v.-;:A. It was unp.>s- 
^ibl. t.. ..l.tain .linu.tly tlu' nu-an pri.H's tor wln.^h the 
annual pr.>u, .,iou was snl.l, an.l .■nuHMiuontly Uumht- 
..ontago .'han,.- in th.. n...an pri..- .•-.ul.l n-.t ho cnu- 
put.Hl .luvtly. Th.. .l.'vi... that was utdiml t.. up- 
p,.xinuue thcs.- ,H.n...nta,.. .•hati^.'s is illustraUnl m 
T.U.le V ..f tlu- A,.p..n.lix. As th.. .lata u.hhI...! f-r the 
sc,hiti..n ..f th.. pn.l>l...n wcr th.- annual pem.Uase 
changes in th.. n..an pn..e an.l n... th.. actual niean 
annual pn....s th..n...lv..s, it wa> n.,ar.l...l as suh..u.nt 
for .mr purp.>s.. t,. suhstitut.. for the unol.tamaM.. an- 

,^„^^, ,,,,,„nta,.. .•han,..s in the nu.an pru'e. the nu-an 
^,,^,,.,1 p..n.enta,o ehan^.-s in the pn..es .>f n.pre.enta- 
tivekin,ls.-f,.i^-iron. Th.. annual prices f.>r the lead- 



114 Krantntiir Ci/rlcs: Tin ir fjiir din! (^dusr 



iiili fdiir kimls 111' piti-iiiiii were dlitiiiiicd li'oni tlic Stulis- 
liral Ahslnirt I'or I'.tl'J, p. 'u'2. ami tin' animal pcrci'i.taKC 
cliaii^ii'^ in the piiri'> (if the luur kiiHl>, tniictluT witli 
their inc:ni annual piMccnlaiic (■lianiic<. an- ji'iNcii in 
Talili' \ nf ilic Appendix. 'I'lie xT^nd ami la>t columns 
(it' Taiile \ uefe u>ed in ('(impuiin^i the law ot demand 
tdf piii-ifdii in the I'liiled Slates. 

'I'lie ^fapli III' llie law of demand hir piti-ifoii is ^iiven 
in I'i^Ufe -\. Tlie ('(irrelalidn lielwe.ii the percenlay;e 
chaiiu^e in the jiroduet and tin pei-ceiitatic ehaniie in the 
pi'ice is r - .'t'.\7 . The (([Uatidn td the law (if demand 
is /y =•..")•_' 1 l.r !.")><. the (ifijiin lieinu' at {o.oK Our fe- 
presentati\-e (■r(ii)s and fepres'iila* i\ c prudurers' ^(kmI 
exem[)lify lyjies nf demand eer\ cs of conti-afv (•!iafa<'- 
ter. In the one ca-e, as the pi'oduct increases or de- 
creases the price falls or rise-, while, in the other case, 
the price rises witli an increase of the iirodiict and falls 
with it> deiTcase. 

The two preliminary dilliculiies are imw cleared 
away. We know that as the yield per acre of the crops 
increa.-es the |)hy>ical \dluine of trade for |)roducers 
^oods increases; and we know, furthermore, that the 
Law of demand for a rei)reM'ntative producers' (^ood i.s 
<uch that as the product increases the jirice increases. 
If now a third fact, which has already heeii cstaMished, 
he added to tlie>e two. an hypothe-is conformalile to 
the three t'acts ma>- lie made which will ^:ive a workin,.;; 
theory foi' cNaminin^ whether he cycles in crops pro- 
duce the cycles in p'lier.al prices. 'The third fact to 
which n^ference is made is that the law of demand for 



Tin Mirhdiii.'^in "J r//(7(.s 



115 




UO^I 



'^^-^idjo /jud^H^ u, P^uenD Jetujy^^d 



110 lu'diKimii- Ciirhs: Thi ir f.mr iind Cnuse 

the cn.ii- l":ilU dmiim a pcriml nf i":iHiiiir ^riMicral prices, 
ami rises duriim a pn-iiHl df li-mti ^cncfal pricr-. \\ ith 
tlic-c fact- in iiiiinl it i- ii'it ililiinili In cMiiccivr how 
gi'licral prici-; iiia\- fall diirinu a pfiioil nf diiiiini-liiim 
yield per adv >'f the ci-niw and ri-r durinii: iIm' imtkkI 
that thf \icld i- iiLciva-iiii;-. The talhim yield in llie 
(•[•ops would lead to :i diiiiiiiution ot' tin' voluiiir ol Irade, 
!i dcrliiic in the diMiiaml I'or pi'odncci---' »n>»\<. a lall in 
the priec< ot' producer-' y;ood-. a. decrea-e in employ- 
ment, a fall of the ilemand cur\e- I'of iToji-, uith the 
final re-ult of a fall in ticneral price>. >innlai'l\-, a 
rising \ ield in the cro|i- would lead to an inciva-e ni 
the \oliime iif trade, an increa-e in the demand tor 
l)ioducer>' }iond>. an increase of employment, a li-e 
in the demand (Mirve> for croix. with the luial re>ult of 
;i rise in ^naieral in'ices. l'ro\ ided the interrelation of 
the economic factors are in accordance with thi- de- 
sci-iiuion. then it would toll.iw that the cyclical move- 
ments in the yield of the (M'op- -liould !»■ I'eproduced 
in cyclical mo\ement- of ticneral jirice-. It the actual 
facts l.eai- out thi- deduction, there can lie no doiiht 
that the cause and law of economic cycle- h.ave heea 
di^coxcrcd. 



Tlic Funddtnoilnl, J'l r.^ish nt Caiisi i>f Ei-(iiioiiiic CijcUs 
To put th(- theory to the te-^t of facts we riMiuire an 
index number of general price< throu^ilioul the period 
covered l.y mo-t of the inve-tijiatiou in this Mssay — 
the p(-ri(Hl from ISTD to I'.tll. There is no one index 
number covering this perio<l for the Cnited States, hut 



77,. M<rl„inisni I'J ' >7p» ' ^ ' 

V.rvf..r.unal..lv.h.T.:MV,vv„.-n..~.l,:.....rl:.,Mn.!H. 

;,,!,,., ,f ,,,,,,.,,,,,1.-... In- i'M—'i'i" ""•••-"•'"•'=; 



III! 

l,.M,uint«ri-- in M'l'-''"" ="■'■"' 



UK 



• tl,,. I'l.lkncriu'lcx fur "all 
,,,i,,l,."..x,..n,ln,«.n»nls7U...lsMn.:.n.l.lH.n.l.v,.f 
;,,,,,,,,... .fl.:,l,.rfnr ••all. •nnnu.M.n.^''..s.>.Hl.n« 
f,,„„,S.,0,ul'.n. S,„n.,lH....-.hav..,!H.v,.ar s,H 

inn.unn.u.tM >1,1.., Lv aiM-Kn,. .!.■ -npl. rul. . 

pn,,....m,.on.aun.,lH. lalkn,.~M-^'n,h.. .a..uf 

t,,. -,,,,.. puMi^lH.ai>v.l...i^un.aunn.al...r. Ih-.tw,. 
o,i,inal.m..^au,Mla. -n,n,uuu^>.-rH.san. ,>v..nm 

•[•.,1,1,. VI,, I ihrApp'^'i'li^ '"''"- '■''■'''"''■• 

-n,„ ,..., „f ilH. ;!H.Mrv ,!,at -1,. ••au-. an,l law m 

('(■i,ii,,ii\if cvi'li- ;"■'' '1' 
vit'M p,"raciv.,f the I'mp 

|,i,.,, .„,, ,!„■ .l,.vialinn~ of tl>r uulic- - 



„. ,.y.'lical in,>v,'ni>-ut.- nf ihc 
w will hciiivcn inan-wcrt,, IW' 



^,„..,-al pn,...^ fn.n, .h.ir ...u.ral .v.U.al .n,.nn.n 
..„,n.la,<.awnh.h..a,.v,a..n,.nf,lu.,n<lu..^oMh.yu.M 

p..ran^.nf,h..n,p.rnnnth..r,..uH.al.yM.'aliu.v..- 
,„.,„•' S..,.n>ullv,an-.lH.ryrl.^nfpnr.sa,.4-h..-v-lr. 
.,f,,„psn.nTla,..a-' Tl,. an-wvr^ t„ th..- . w„ nrn'M pms 
•UT tl,.' Mil.stanrc of tlu' fnllnwinii parai^raph^. 

,„T,l,l,..lllauaVl.>fth.'App.'n.lixt,.lh.>.-hapt.T 
,,,,.v..utl,.MU.lu...<.>ftlu.yi.^l.ll-a,.n...f.h...^n.l- 

,^,,,1 ,1,. „,li,,, .,f ^..n..ral pru... TIh. lal,l..< Uk.-- 
;vi<...mta,u.h-..no..tlu.,liu.li.'.'sau.ltl....l,.v>at,ousof 

the a...ual iu.li.^.'^ fnuu tl... M„...uh...l ...[..•.■^. 1 1^^ 
s.n.,oth...U..n..w..n-o!.ta,.u..ln,,h..n,au,u.r that was 

deBcnbe.l wh... th<^ r,.latl.,,. l..tw....n .h.| y,..ia ..t lu- 

,,.ops ami th.. ,H-.Hluctu.u of pig-iron wa. iKUUg tn.at..l. 



118 luiinntnn (i/ilis: Thiir I .mr iiihI ( 'dllsi' 

If will 111- itcmIIimI fri'lii tli;it (!i-ci-i|itiiiii lli.if flio 

>i I licil iiidiA ti 'I' ;iii\' ^i\ 1 II \ I .-ii' 1^ I lir 1 1 II 'nil of l luce 

;ic'lll;il illilirr-: till' ;irli|;i| llnliA t"l' llir ^:i\i'Il \c;ir. tlic 

;iflii:il ihiliA tiif till' \i :ir priTci!!!!!; till' (iuiri Miir, jiiid 
till- ;iriii:il iihli \ t'lr ||ic \i ,ir ImIIi.w iii^; tlif )ii\cii >i';ir. 
'I'lii- qil:ilil It 11^ wlin-i- CMiTrl.il loll i> ill (|ilc^liiili ;ii" tlic 
(l('\i;it li Mi^ 111' I he ;irl ll;il ilicllrc^ i<\ \h\\<.Va\ |)I'i( ■(•-•, Illul (it 
yii'lil |Mr Jicii-, llMiii tliiil' li'-prct l\ I' Mliuutlhil M'1U'>. 
'I'lir Ic.-llll- III I lie i(>lll|il|l:il mil arc ;i- l'iill()\\>: 

Inn,, |s7ii I'll I, r = .;{«J, 
Fn.in 1^70 IMill. r - :!7(), 
lv.)lli 1MM»-I!t| I, , -.JJU. 



Ill the lii-t low the cdriTlatioii^ were dlitaiiicil fruin 

tlic cnlil iliUolls Miles ill vvlilrli till' IlllklliT iliilrV Wa- 
il' l.|ll~lci I to ihr imlrx (if till' r>iiii'au (if '.almr. In the 

M'ciillil Inw the CnlTrlat iiill> Wi'lr (li'rivcil flMiii till' 

i'alkiicr !ii(li'\ iiiialliTi'il. In the tliinl I'mv tlic ciiiicla- 
,11 lis Wtif •iinliuli'il IViiiii tli(> ' A' (if tlic liiirrau (if 
Laliiir. \\ I' inlcf that till! (Ic\ iat Hill- fnuii tlii-ir <iiiiri-al 
cyclical iiiii\ (iiiiiit (it tlicjiiiliccs nf liciicral prices \arv 
directly Willi tlic de\ialiiiii fiMin tlieii- {iciicial cyclical 
li|ii\ ellielil 111 the indices iif the yield pef acre of tilt' 

Cllip-. 

The M'cciid iif the two (|iiestions as to tli(> (•aii>(' and 
law iif the c.clcs of (.'vneial places was stated in this 
form: Arc the c^cf s of prices and the cycles of (aop- 
correlated'.' 'Ihc p/ecediny; paraiiraphs lia\e pre.-ented 
the re-nlis nf tic in |uii'y as to ihc i-clatioii lieiweeii the 
(le\ialions of actual prices and of _\-iel<i from their 



Thr MirlKini.sm of ('!ldt'>* 



119 



,.p..Hiv.. p>M..rnl .•vHi.:,l >„....,-,..„. 1 1,- pn-nt 

|i;i\C liccll I lllllM.-lli'il 

■|,.,1,|,,, :!M-..r,„T;,l.-vr!lr;,lin..V..,„rl,N 

,v :, ,,p.r..- ..|- -nin-.thmii 'I'- :"'u;,l 

proooss nm>.stiu, u. -l... f.-vn,:,-,.,. ,. a ,.rn,n.>^iv.. 
,n.nnof,h.-in,li..^i..n„- n ,v„„v.. yoars. I u-sc 



ll w ill \«- li'i-:il 
Wric i)lil;il';i ll ' 



litccl in I'lli- 



piv-nit iii\(-li'^;iliiiii. 

Tll,. thn.l Ml Ilir HlV.MiliMti.'ll i^ IT' 

^„.,.,.,:, ..,-, ._.7. Inth.. liM „, ,!m~. ilnr.. 1 ,Uinr~. .hr 
..,.,H.r:,l rvrli..! ,„..,.,„.».- n, prnv^ :m.l n, v-.M ,-r 
,,,,„,,„:i„..nl...l:u-r,ln,. .iMlH. .la.a.l laM.^H 
;,.., VI TlH. .rapl- 1-n. nu. -•l.arU , h. rhv,h>nu-al 
' ,„,„n^ Ml- l,n,l,. pn.T- a,Hl v.M a.nl a nuni-arM^n 



lliul 11 



i- :i laiililliU 



nrt!,r,Mirvr~M,-rM^tli:.t 1 1,,' pnrr rl.rv.- 

,,.„,,„.,„„ ,,,l...yi.l.ha.n.. Hu, l.-f.-- tl>- aii.-unt 

.,f „,.. hm ana Ui. ,!.•..- .1- r„m.l:ni,.n l.-uv..... th. 
,v..l..,.anl..n,n,,n>,..,l. .h.'-nlar.n'na^n, ,ln.,^v„ 
..,H.-^f^:.lu..^.nuMl....lnnlnan..l. 1-n.n, H.un.-..>t 

is apiKUvn- .iKit th. pn... ryrl.^ n,nv.. upon a tailing 
....ular .mi.i uli.lr .lir VH.M ryrl..^ .11. v.. up.m a r.Mn^ 

<..,.„lar.m..l, int,^a^Mnn...la~aiiMa,>pn.xnna..on 
„,.ltlH.~r>.Tular..vn.ls an. 1...11. linear,. l..-,,ual.nnU. 

ll,c ircud t..r i-nn- i> '/ - ■•^'"-' '- . 

tn.nd P.rth..vH.Mp..r am.,, ^.!S44.r4-^K;^7. .!.<■.. n- 

pn,>u.lH>runn..rra^.,lH.in^a. 1S7;^ and, in th. la.t.r, 



120 



Kranur,,;c('iir!>< Thrir l.mr and Cnnse 




•«.•>;■,<-■'-'■'>'""'"'' ■'■'v-""-' P^' ''"^->-^ -"'-*' '-"^^''' ^'"''-^ "''"' P'-'-""""^ 



The McrlKini.^m <'/ ('ndcs 



121 




tdojjjo ij}e -Jii 






122 Economic i yclrs: Tlicir Law and Cause 

:it 1S7I.' 'I'licsc two (MpKif imis make it possihli^ to 
cliiniiiatc tlic scr-ular ti'ciids upnii uliicli innvc the 
cyclf's (if pi'iccs aiul the cycles nf yield. The results of 
the calculat idiis aic <X\\vi\ iu Talde \ 11 <if the Appendix 
to this chaiiter. 

I'iiiure ■_'•) preseiiis I he cycl(>s of yield jiei' acre and the 
c\('les of jieneral i>rice< after the secular trends u|)oii 
which they wefe i'es|>ecti\'ely su])efpii>e(l ha\'e lieen 
eliminated. It is ([uite evident, now, from the .appear- 
ance of the ^ra()hs, that the cycles of yield jier acre and 
the cycles of {lencrul i)rices are closely relai( d. and that 
the cycles of prices lag several years liehind the cycles of 
crops. What is tlie atiiount of the lau and how closely 
are the cycles correlalcd'.' I'mth of these (|Ue-tions may 
lie an>wei-ed at once iiy following: the iiKthod that was 
adopted to mea-ure the lai; in the c>'cles of pi^-irou 
production. If the cycles of the \iel(l per a<a'e ;ire 
correlated - with the I'ych^s of t':eneral prices we tind, i'or 
a lav, of three years in general i)rices, r = .7St); f<ir a la^ 
of fotu' years, r = .S()(l: for a lau; of five years, r = .71(). 
The cycles in tlie yield \)rv .acre of the crops ar(\ there- 
foi'c, intimately' coiuiecled with the cycles of ^oiHM'al 
prices, and the !a^ iu the cycles ot general prices is 
approximately four year-. 

Figure 27 prc^etits tlie two set ies of cycles with th(> 
lag of four years in the cycle> of jirices eliminated. It is 



'The first cciualion wa.-' t'dinputcd fidni thi' data fur IS".") 1!H0, 
and the ticeoml ((iiiatioti, frciin tlie data fer fN7f- !'.•()(). 

' Tlic data for the calculation are piven in idlunm.- 1 and 7 of 
Tabli- \'li in the .\iii)cndi.\ iu tliis ciiaiilcv. 



TIk M( rlidhisin nf ( 'yrhs 



123 




ijjp ^aJ rijiX auj. JO tjpui jl// ^o s-j.ujujjaolu jPJi/oAd /p^juj^ jlj^JO suc-^piajQ 



iL't Frnnotnic Cycles: Their Lair aiul Cmise 



Mircly 1, i aiK'xaMiflfratinii to say ll.at tlic cniijiruciicc of 
iIh' two rliytliiiiical iiio\ I'lnciits of cfoi) yield and jiriicfal 
J)rices is so close as to justify the iiifeiciice thai the v>iie 
scries is the eatise d the other. I-acit iiiipoi'taiit 
rhytlitiiical feature of the yield eui\e is icprodueed in 
the price cur\-(>: the Imiiz: cycle wh.ich in hotli curx'es dips 
I'eiow the horizontal lietween ISSO and I'.IDO, and the 
smaller >uper|)osed cycles that nio\c upon tiie larfj;(> 
Hrouiid-.-\vell. The one ajjparent excepti<in occin-s in 
the price ino\-ein(>nt iietween ISS7 and IN'JI in which 
the price curve does not keep closc^ to the yi(>l(l curve. 
lUn tliis is not ureal excoj)ti()M. For. in the first place, 
<lie price curve is convex hetween these limits, that 
is to say, it shows a tendency to conform to th(> yield 
curve; and, in th(> s(>cond place, since in the price 
curve a lajj; of four years has Iummi eliminated, the date 
at whicii the distiu'liance occurs is r(\dly four years 
later than would appear from the dates oi, the chart, 
'i'hat woulil place the disturl)anc{> .at aliout ISOIi. which 
was the year of the j^anic with extraordinary condi- 
tions in the -tate of the currency autl tiie money mar- 
ket. 

< 'oiisiderinji the hiy;h correlation between the two 
scries of cycles and the harmony of their conjiruence 
with the theory of (economic cycles etiilxuiied in this 
Kssay, we conclude that the cycles of the vield per 
acre of the crops cause tli(> cyc'es of fjjeneral prices and 
that the law of the cycles of crop.s is the law of the cycles 
of general prices. 



77/r Ml rhdiiis/n i>f ( ' ijch : 



125 



Tho chief results of itiis cliMptcr iiuiy lie Miiniiintizcd 
in a few propnsitiiins: 

(Ij Tlie \ieM per ;icre. fur tlie whole ni the I'liitrd 
States, t>{ the t'liur repre-eiitati\ c ei'np-, enrii, 
liav, (lats, nii'l p()tatne< i< so closely enrrelatcd 
with the yield per acre nf these crnjis in Illiiuiis 
a- to rendei- it \-ery prodahle that ttie eau>e of 
the eyele< of the yield in the I'nited Statt'S 
is the same as the (■;!U>e of the cycle- in Illinois. 
'I'he meteorological cause of the rhythmical 
chaniies in the yield of lUinoi- has lieen <lis- 
cussed in an earlier chaijter. 

(2) The i)riee> in the I'liited States of the four 

repi'esentati\ (• crops are as clo>ely related to 
the yield per aci'e of \\\v crops as the prices are 
related to the total >uppl\' of ihe re-pective 
eroi». I'or the i)urpo>e of p,|-ediction of pi-iccs, 
therefore, tlie yield-|irice eur\-e is as usetul as 
the demand cm'\('. 

(3) d'lie cui'ves i-epi'e-entins the relation l)et\V(M-n the 

yield per acre and price, in ea-e of the four 
represent at i\-e crops, t'all durinii a period of 
falling;; yield and falling; jieneral prices, and 
rise under the conti'ary circumstances. 

(4) The falling oi' ri>in^ yield ])ei' acre ^^i the crop;j 

leads to a falling; ov I'isin^ \-olume of ir;;de in 
producers' ^oods. If tlie production of pi^- 
iroii he taken as a representat i\e jiroducers' 
frood, tlieii 

(,a) Tlie deviatiou.s oi the annual production 



12(i ludniitiiii- ('i/<ic.s: Their Lmr mnl ('(iiisr 



(^; 



(/ ) 



"t |)i;;-ii-Mii tVoiii the liciirnil cyclical 
iiiii\('iiiciii ill ill,, prddiictic, (if piii-irnn 
ai'c diivcily ci inclalcd with 'lie licvia- 
tions, in the pi-cccdint: \(ar, <>( tlic 
yield per acre of the crdp- tVcini ihcii' 
Kciicral cyclical iiin\ ciiicnt ; 
(b) When the laii in the pi'dduclion nf pijr- 
ii'"n Jtnd the secular ticnd in hnth the 
produciinn nf pii;-ir(in and in the yield 
pel- acre of the (■vn\)< aiv eliniinated. tiic 
cycles <it pi-ndiictidn (it' pii^ iron are \erv 
clnsely cniTi'lated with the cycles nf tjio 
yield i)er acre nf the crops. Tlie cnejli- 
cie-it (if cdin iation i- ;■ - .71!). 
I nlike the law nf demand for the ci-ops, the law (.f 
demand dn- a ivpiv^entat i\-e pfod.ii'ers' trnnil 
is such that a- the -iipplx' iiicivases the price 
rises, and as the supply decreases the prico 
falls. 
\\ ith the falling (u" the yield per acn> of fli(> crops 
there is a fallia^^ xolume of trade, a fallinjr 
pric(> (,f pro'iucers' '^luxW. an increase in uu- 
emi)loymenf, and a fall in the yiejd-iirico 
curves for the crops. The conti'ary conditions 
prevail under a risiim yield per acre of the 
crops. 
'I he ultimate effect upon general jiriees of tlie 
j)roeess descrihed in (Ci) is that 

(a) 'Ihe deviations of general prices from 
their g(>neral eychcal movement are 



Til Ml <-li<ni 'Sill (if ('!/(■!( s 1-7 

ilircctly ciii'i'datcd willi llif dcviiitinns 
(if tlic yield per acre nf the crnjjs fnun 
A tlirir liciici'al cNclical iu(i\('iiiciit ; 
il)l When ihc his, in general jiriccs and the 
s. riilar ti-ciid in Imtli pi-iccs and yield 
])er arre are eliminated, the cycles of 
jieneial prices are very closely cnrre- 
lated witli the cycles cf the yield per 
aci'e of the CiOj;s. The coefiicieiit of 
ciii'i-elatioii is r -- .S(l(l. 
(8) The law of the cycles of cmiis is the law of the 
cycles in the activity of iiidusiry and the 
law of the cycles of fjeueral pric«'S. 
(0) 'idle fundaniental, persistent cause of the cycles 
in the acti\ity of industry ;ind of the cycles of 
general prices is the cyclical movement in the 
yield per acre of the crops. 



128 



Kcunntnir Cijrl,.: Thur J.air and Can.st 



APPENDIX 



•\lil.i: f- Im.kx \rMi„:u ny ni,. V,,:,.,. p,,;,, .\rHK uk Chm,.. 



\r\n I Im>k.x mji \sin.x fur 

NlNK Choi',. Fill It fKops 



l^nt I 108 

In7I Id,-, 

l-^"- Mil 

is7.: !M,i 

1^71 ss 

|s7."i III) 

l^7ii Its 

l>-77 Km; 

1^7n II IK 

1^7'i 111 

1^''<» IIIC, 

Issl sj 

1^---' l(M» 

l^^'i !I7 

l^-^t III! 

I^sfi !!> 

l^^7 sd 

1^^"^ IIMI 

l^'>'' 1(11 



V f » K 



Indkx roR I Index for 
NiNB Choph'K.mh Cr.ips 



ll)<l 


' IH91 


lOS 


i 1117 


ll.i 


|S!)_> 


!IS 


!):i 


11.-, 


lMi:{ 


!'.' 


!•.-> 


!ts 


iMIt 


(Ill 


S.') 


•SS 


IMC, 


KlJ 


Idt 


III 


iMMi 


MIL' 


111 


1(11 


IS! 17 


Id.' 


II IJ 


III) 


IMIS 


Ill 


Ids 


li:; 


is',l!» 


Id,-, 


Ids 


Ml 


l!MI() 


Idl 


1 1 1.-, 


1117 


I'.tDl 


.V» 


s.! 


^J 


l!ll)J 


lit 


117 


!»!l 


l!l(l.{ 


Id7 


111 


ilK) 


I'llll 


11 1 


117 


1 1 1:, 


I '.III.-, 


Hi; 


l.'l 


II L' 


I'llMi 


11!) 


IJd 


!i:i 


11107 


IdCi 


107 


N.-) 


11 MIS 


ld!» 


110 


lo:) 


HKI'.I 


Ids 


111 


loi; 


Hull 


Id!) 


1 r> 


m 1 


nui 


()!t 


it.-, 



Tin Miclidnisin <>J (ijcus 



129 



TAIU.K II. TlIK (iKNKHAI. Cvci, 

^•^:lt^;^(■^:s ok ihi; I'liDUiriK jn 
Si \ 1 1;> 



I(\l, Mn\ KMF.NT AM> I'lK DlF- 

cii l'h;-lii'>\ IN nil. I'sni;!) 



Year 



PRf»orr- 

TION f>F 
J'lll-IRIIV 

IV Tiiin- 

r*ANt>H OF 
I.OMI 
'I'. I NX 



|S7I) 


LUti.') 


I.STI 


1,707 


1872 


•J,.". I'.t 


1S7:{ 


2,.")r.i 


1S74 


2.101 


is-:. 


2,0-' 1 


1S7C. 


l.sii'.l 


1877 


2,0t>7 


1S7S 


2.:ioi 


1870 


2,7 IJ 


1SS0 


■As.;:. 



I^s| 

1.SS2 
18S3 
ISSl 

iss.-, 

1S,S(> 

1S,S7 
1S,SS 
1SS<> 

isno 



),l II 

4,ti23 
4,r>'Mi 

-t.oos 

4.0 1. "> 

r),(>s;{ 
(1,117 

(■.,(',10 
7.C.!)l 



I IJlFFEB- 

Phe Ges- en<-k Bk- 
kiui. c'v- twef..n 

II.KVL j THE .\c- 

MdVE- I Tt Al. 

MK>T I'l 'lurr- 

(PR(»(iHE«*- TION AMt 

1 »1VE Av- TIIE C'lEN- 

'EKAOErt OF KHAL ('\- 

IThUKE 1 CMCAL 
Ycauh) .Move- 
HE.NT 



l.'.iTt 
.> ■)-■> 

2..">04 
2,:i2(t 
2.0!IS 
1 ,'.l^7 
2,07<.» 
2.;{7() 

2,t;.'ii 

:i..".7l 
1..' 11 
4.i:.4 
4,4:w 

4.211) 
l,t')0',l 

."i.:i->2 
ti.l',t7 
ti,^:i7 
7.7t)r) 
s.-MVI 



+277 

-f ru 

+ 72 

- 7t 

lis 

- 12 

- Ii',1 
> 110 
- -'lil 

+ 1011 

+ l.-i7 

-1 Is 

.",01 

-:;oi 

-220 
:U7 
102 

-rM I 



Yeah 



I'kouit- 

TIOS" OF 
I'KllRON 
I\ TllOt - 
r.AVD!4 OF 
I.ONU 
'Inst 



The Ges- „ 

tUAI.<V- „,K^.T.,.t 



Is'.M j 
1VI2 } 

l.sou i 

IVU I 

IVI.J 

IVHi 

1MI7 

is; I' I 
I'lOO 
l',IOl 

1:102 
loo:< 

l',IOt 
1!I0.") 
I'.tOii 
l'.»07 
l!tOS 
1!»01» 
I'.ilO 

r.ui 



s,2so 
(M.'>7 
7.12.-> 

(),r).">.s 

9.4411 

K.ii2:f 
'.•.o."):< 
11,771 
i:i.021 
l:i,7y) 
l."i,s7s 
17,s21 
is, 00!) 
111,107 
22,002 
2'>.:io7 
2-),7sl 

i.").'.,';iti 

2'),7(».") 

27,:!Ot 
2i.ri"iO 



ri.i(-Ai. 

.\IoVE- 

MKNT 

(PkooUE! 

hUB .\\ 

EKAiiKH <i 

'^MU^.B 

Yea Ha) 



S.SM) 

S,|s7 
7.i>17 
7.7 i:i 
.s,212 
•1,2 1 1 
10,017 
ll,ils:{ 
ri.Oiil 

1 1,I2'.I 
l."),s2'.) 
17.2:iH 
17,112 
10,100 
21,.V.I'.t 

2 1.00 i 
2.>,:'!ll 
2 J. .Mil 
2:5,012 



AlTlM. 

PliOltlO 

TION AM> 

THE CJes- 

EKAL {'v- 

. CI-ICAL 

MovE- 

HK.ST 



— C(K) 
-f 970 

- - .122 

lOs.-, 

,12 11 
OIS 

- :ii;i 
+ 01 
r-im 

tilO 

40 

."js.-, 

+ r)07 

2tl(l<) 
-t-lH9:i 

+ tilt 

+:sii() 

+27s:{ 

+ 1721 



+ 
+ 



l;lt» i:vu„„n,ir ( urles: Tlu ir Law aud ( a 



unc 



■l'\l{ 

1 1; 

N'iNK ('urn- 



In.; (i,:s,:,„K (•>,,,. A,. M„v,.M,M ^^„^,^.J).K- 



Vk:AR 



Index m 
I'tR 



l"B Ciitx- T)in>.i,- 
tim. Cv- ! r.si y. Id 

''•"'•*'• >» KIN TIM 
•MllVE- AlTIAI. 

, „*"-^T 'Indkx Axn 1 

ACHK (F'KIMiHRH- TllK(il:v- ! 
(NlVK HIVK Av- KHAL Cv- 

l miPK) tHiciKK ip> riiiAi 

TllllKK I M.iVK- 
( > EAKi.) I MKNT 



Veaii 




liii: (if V- DiKiH- 
1 Mui. Cv- ,:v, K ItK. 

IMltXOF <lir,|, TMKKNTIIE 
V1M.U I .\|„v,> A.TIAL i 

I MCXT KOKX AND 

'Priiuhkh- thkCkv- 

»r»K AV- IKAL Cv- 

himiKu or (i.iiAt 

'IllMIK .\l.,^^> 



Tkh 
AniE 

'Sink 



(IS ,{ 

'x; :{ 

!M 7 
IK (» 

111.' I) 
In:, II 
km; 
lOii 7 
'.III .{ 
111." .( 



4- !t 7 

- I .{ 

I :: 

I 7 

r 1 l> 
(I I) 

:; 
+ .■. I) 
- 1 7 

+ •1.7 
i:{ .{ 



In:; ;! 
1117 


r in 7 
1 7 


1 1 .' :i 


- 1 7 


lir, ;{ 
1 i:{ 7 
III :! 


:{ 

f r, :{ 


11)7.7 
I OS. 7 


+- 1 ;i 

— .7 


105. .3 


+ :i 7 



7V(( Miili(tinsin nf Ci/rlrs 



131 



\i'.i. 



|\ ( Vd.KS 1)F ViKLD I'KU A< UK OK (KOI-S AM) < 'Vl I.KS 

ur I'ltmn iTInN UK I'lil-IKiiN 



(iKNERVI. 





1 iK\rH\i 


1 


, 


• 'tii.um. 1 






(ICI.KAI.,, „ Ct.I.M M.IVEMBNtI 


Ordinate ■ 


f'Tri.ri* or 


Mt>\ K- 


UK Tll>. «y ViKIll or I'H"I>1<- 


DrTHE 


'HnlH'i TltiN 


Vkah ttr.sT 


<>:rll\H I'KH Ai IIK THIN OK Pill 


Se< fUB 


tV I'lil-lltoN 


or Viv.i.ii 


Thknu lit <K'ii-i ihi>s. in 


Tbknu 




rt.H AtHt 


' TlInt'«AM>lt 






.rOir* 


iiK Tl>S« 









_ — 1 




' 


I,S7I 107 7 ! 


0> t( 


+ 1 l.'t71 


- i,:i4f. 


+ 3,.')20 


1S72 


10» 7 


OS H 


+ r. 1 2.272 


- IMIJ 


+3,230 


1s7:j 


00 (» ; 


OS 9 


-1- -l ! 


2,.'.oi 


- 3Sl 


+2,S.s.') 


1N74 


09 


00 1 


- -l i 


2,320 


202 


+2,127 


is7r. 


9S.7 


00 3 


- .4 


2,09S 


7S4 


+ 1.311 


1K7t5 


im 7 


00 .', 


+ r>.2 


1.0S7 


1.307 


+ 020 


1S77 i 


104 3 


00 7 


+ 4.<) 2.079 


l,9."i(» 


+ 129 


1S78 


10S.7 


00 1 + K.S 2.370 


2,.')32 


- 102 


1S79 


lOH 7 


KKIO I 4- 8.7 2,02r. 


3,11.") ; 


Is'i 


ISSO 1 


9t».7 


100 2 — ■') 3.."7t 


3.()0S 


IJI 


issl 


giro 


11)11 I II l.-'iil 


I..N1 


so 


1KH2 


93 


KM) f. 7 'i t.l.'il 


I.Mi.l 


40'.» 


1883 


09 ;{ 


100 1 '■ I.13'.» 


.'■), II'. 


1,007 


1KH4 


9S.7 


101 — 2 :. 1.20'. 


ri.oj'i 


l,7s3 


1885 ; 


97 3 


101 2 — 3 9 4.C.0'.I 


O.i'ill 


2.(M)2 


188« \ 9:{ :{ 


101 3 , - SO •">.3s2 


7.1'.'l 


1.M2 


1887 91.0 


101 5 i - 7 .') O.l'.tT 


t .1 1 i 


1 ,.")M» 


1HS8 


07 7 


101 7 1 '• '''.s:!7 


.S.oliO 


1 ,.')23 


ISSO 


'17 7 


1(11 I.I - t J T.Tiiil 


S.042 j 


-1,170 


IsOO 


liM) :{ 


102 1 1 - l.s s.iii.J 


"..">2.") 


— l,lt)3 


Is'.tl 


'.IS :{ 


102 3 — 4.0 S.HSi) 


lo.ios 


-I.22S 


lh92 i Oil . ;{ 


102 4 ! — 3 1 s.IsT 


lu.ii'to ; 


-2..')03 


isoa 


93.3 


102 « ' — 9 3 7 lii: 


1 1 .273 ' 


-3,ri2i) 


1S94 


94 7 


102, S —81 7.7 1:'. 


1 1 ,s.')C> 


-4,112 


1S95 


OS.O 


103 — o.d s .MJ 


1.M30 


— 4,l'.t7 


1S0<> 


1020 


103 2 ■ I 2 0.211 


i:!,i)21 


-3,7S() 


1H97 


105 


103 1 -r 1 •' 1""1' 


13,1.1)1 


--3,.")S7 


1S9.S 


KXi.O 


UK 5 i + 2 .'i ll.tis3 


1 I,ls7 


-2..")04 


1S99 


Km 7 


103 7 


+ 3.0 13.0111 


1 l.r'.'i 


-1.70S 


1900 


09 3 


KW.O 


— 4 ll.»2'.> 


l.".,:i.")2 


- 023 


lOOl 


102.3 


101 1 


— IS l.".,s2'i 


1."..03.") 


— 100 


1902 


103.3 


101 3 


— 1 I7,j::'i 


lll..')lS 


r 7IS 


IIMKJ 


111 7 


KU..") 


+ 7.2 17.112 


17,1m ) 


- 312 


1904 


112 3 


101 7 + 7 1) I'.Milil 


1 7.(1^3 


-)-1.4v3 


lOOo 


! lie. 3 


lot S ; 4-11 .-. 21/)90 


1 >.2l'.() 


+ 3.333 


lOOti 


1 !'■> " 


10.-) O 


+ S.7 1 21, ('.93 


1S,S4S 


+."),s;') 


1907 


1 1113 


11).") 2 


+ 1 


22,341 


10.431 


+2.910 


190S 


i 107 7 


10.", 1 


+ 2.3 


22,.'^01 


20.014 


+ 2.400 


1909 


los 7 


10.") .") 


+ 3,2 


23,012 


20,.59t) 


+ 2.410 


1910 


ior).3 


KIT) 7 


— .4 


2.5,5,S3 


21,179 


+ 1.104 



132 

Tvi;i 

IKON 



Economic i'm-Us: Their Lair ami < ,uux 

.1- \ rKKCKNTA.iK ClIAV.iK IN uif. l'|i. .Ul ."rioV OF Pi.;- 
AM) MkaS I'KlirKNTACiK CllAN-.iK IS ,IIK I'm, >; OK l'l<i-|„oN 



TIIK I'llO- 



Pkhcknt- 



l'» K< » VT- 



••■■»■•■'" '^ * r 

AT l'lTT»- I'lnsui-Hd 
Bt'NU 



I'lii ini.v 




'/■//, \hrl,a 



I' ( 1^1 hs 



\XA 



TAIU.i; VI. TiiK Im)K.\ Ni Miii.u uy (a;\KUAi, Piti< Ks. It.s 

< IKNKIIM. CVl l.lM. MuVhMKNT VM> IH DiKKKUKMKH 



^ LAN 



1870 
1H7I 
1S72 

is7a 

1874 
1H75 
1870 

1877 
1S7S 
I.S7'.) 
1880 
1881 
1H,S2 
1883 
18X4 
1885 
1S8(1 
1887 
1888 
1880 
1890 
ISOl 
1892 
l.S!»3 
is; 1 1 
iyt."> 

IV.M) 

Is<t7 
IVIS 
IMH) 
l'.*IH) 
I'.tiH 
I'.Mc.; 

lUlK! 
I'.MIt 

niiir. 

l'.t(l7 

lyos 

I'.KI'J 

19U 



1 


l!t-Hr:\i' *n 


Kaiknkm- 
l<ill».\ 




(Jknk.hh. 
<'»i-r.ii«i 
Movi:mkni 

or riii: 

t'lllTIXI- 
Ol-i Ivilf.X 


IDirrKRBNca' 

HrT^iLr.N 


1 i'«i.KNr.n «; 
Imukx ok ' 


I.IHiiH'p* 
ImiKX of 


.\ii»f»Tr.ii 

To TIIK 


TiiK Ci,x- 


THH .\lTr\l 

Ini)i:\ «nu 


rHK'KK or 

".All. .\it- . 

TH'I.Kit" 


I'HII'KH or 

\i 1. Cum- 

«iiuiriK»" 


IU->I. OK 

TIIK IIIK 

K\f OK 


Iniikx or 

I'MICE* 


TMr liKM- 

i;h»i <■»• 

riliM. 






1 Mtott 






M',\ I Mh sr 


1 117 ;i 




li:{ .-. 


1 l.t .-. 






I'-'-i '.> 




!.-,(> :! 


l.V) :! 


1 I'.l s 


t t 


' r.»7 -' 




l.V» f) 


l.V. tl 


i:ii 7 


+ .i !l 


1 12-' (» 




Hit 2 


1 1't 2 


l.'iti :i 


1 1 


!! U'.t 1 




itr. (1 


1 HI n 


III 11 


'-\ I 


: ii:j 1 




i:ts 7 


i:is 7 


i:i7 tl 


H 1 


1 KM s 




12S 2 


12S 2 


i:il :• 


.t :i 


! KM 1 




127 7 


127 7 


1211 It 


H 7 


>>>.) '.> 




122 2 


122 2 


122 7 


■"> 


'Mi li 




lis 2 


lis 2 


12:1 7 


- *l .'» 


1IK).<.> 




i:ii) s 


i:{(l s 


1211 1 


ft 7 


K>.-. 7 




12!i :i 


12'.t :i 


i:fii 


1 C. 


1()S -i 




1:52 7 


i:i2 7 


i:ii) 11 


t-2 1 




m\ A) 




12!t 7 


12'.t 7 


I2s 


fl 7 




m \ 




121 11 


121 tl 


121 7 


- 1 


I 


<»:{ i( 




1i:{ s 


li:i s 


ii:. It 


-2 1 


1 


!»I '• 




IIJ 1 


IIJ 1 


ii:i 2 


s 




'.12 11 




1 i:i .; 


11.; :; 


1 i:i tl 


,:i 


i 


'.tl 2 




1 1 .". ■-' 


1 1 .■. J 


III', 


f 11 


i 


!)t -> 




11.-, .' 


1 1 .', .' 


1 1 1 1 


-f N 


t 


'.>- ■', 


lU '' 




11 J '.1 


li:( :i 


1 


1 




111 7 




1117 


lilt 2 


f 1 ■"• 






nil', 1 




IIH, 1 


Hi: s 


— 17 






Ul."> 1) 




lii.^i 11 


1112 r, 


+:i 






!tC. 1 




•If) 1 


ns 1 


-2 '• 


i 




'.»:< t) 




«U tl 


'.i:i 1 


f 2 






<H) i 




'.IK 1 


!t| 2 


— s 


I 




S!> 7 




S!t 7 


HI 2 


1 .-. 


t 




'Xi I 




n.i 1 


HI ■! 


-1 .") 






\n\ 7 




nil 7 


nu it 


■> 


i 




110 .-) 




1 i 1 1 .-, 


iiii '.t 


+:i.ii 




II iv ."> 




II In .-, 


1 lit (1 


-2 1 




IIJ '.t 




1 IJ ',t 


1117 


+ 12 




ll.i 11 




li:; r, 


1 1 : ; _' 


+ .4 




u:{ 




li:; II 


1112 


— 1.2 




11"> 9 




11.') '.1 


1 17 1 


— 12 




i22.r. 




122 .-. 


IJJ li 


- 1 




12'.» .■> 




121t .") 


121 '■> 


+ 4 ti 




1J2 s 




122 s 


I2ii.:{ 


— :{ -> 


; 


12ii .^) 




12tl :> 


127 


— •"> 






i.n n 




!;!1 <i 


! "■ ! 


+ 2 :"> 






I'j'.t :* 




12!i :i 




1 



i;{4 



lunti.nniC ('!/(■/,. s. T/„ ir /.,;/;• „„,/ 



tll/sr 



TAIil.l^ Ml. C., ,.K>n,.- Vn;,.„ I',.,. An;,: ,,kC,„„.^ \m. Cvc.ks 
<||-' ' Ji:\i.i( \i, I'liii I , 




"r riiK TPiK ViKi.n 

•■•Klll.Ml I'm A, UK 

'I'llKNU , UK Cllr,,., 



U 1 



+ 



1 I 



I i; 



1 II 



I r, 



1 I, 



- 1 (I 



+ 
+ 



-11 



(1 1 



' ;i;\t.ii 




niAPTKI'v VI 



SCMMAHV AM) ' ' )\( l.l^IOXS 



Tho^e cycle.-- nl" itcijis (■()Il^^itut(' tic iiaiur;il. niateri:i! current 
wliieli ilrufTs iipdii its ^ui-faee the !;:};iji:i«:. rhvlliinieall 



value: 



uiil i>rices with which tlie ('Coi:i)lii 



y elialifiiUK 
ist is more imincdiiitclv 



Coticerileit 



iiK nimci 



pal ciiiitrilmtidii i>f this I'lssay is tlic dis- 



>V(M'V of the 1; 



i\v and cause d 



f !• 



COUdllllC 



Cvclt 



r 



lie altcriialinri 



rliytliiii in the ;icti\ ity of ('('(uiuiiiic liiV 

of Imoyaiit, ))t.ri>os(>fiil cxpaii'-ioii with ainilcss (icpi'c: 



sion, is causiMl l)V tlif rlivlliiii in 



tl 



ic yK'lil ]i('f acfc oi 



tlic crops; while thf fhythiii in tlie production of the 

the rhythni of chaMfiiiifz; 



crops IS, HI turn, caused by t 
weather which is reitresented iiy the cychrnl changes in 
the aniount of raintall. The law of the cycles of rainfall 
is the law of the cycles of the iMMp^ an<l the law of 
l-]conoiiuc ( 'ycles. 

W'l' shall recapitulate the main stages hy wliich this 
conclusion was reached atid shidl take occasion, as the 
stafjes are re\itwed. to suiriicst the care that niu>t 
\)r ol>ser\'e(l iti inter|)retin^ th(> statistical sieni'raliza- 
tions which I'orin the structure of tlii> ary;uineii I . 

When we Iteiiin to think .-eriou-ly about the cause of 
iv'oiioniie ('y<'les we ;ire jireatly impressed i)y the wide 
diffusion of these cyclical mo\-ements amoiii; the peojtles 
of the Wolld. and the inference appeals to he ine\"itaole 
that there must he some |)hy.-~ical cause at work to 



]'.]{') F.ciDiDiiiir ('i/clis: Tlnir Lmr (unl ('nitsc 



aoooimt for so conoral a movoiiicnt. As tlic most 
fuiKlaincntal need ( '' luankiiid is the iicrd for food, it 
seems proliat)le tliat tlie oliserved rhytlimical economic 
cliaii,i:e- ma>' l)e produced liy tli(> plivsieal cause throufih 
its eifect upon the food supply. It tliis !.(> so, tlieii, as 
the tiuctualions of the food supply ai'e known to he 
sultject to tiie supi)osed caprices of the \V(>ather, it 
seems not unhkely that the physical cause may \tv one 
or more of the elemental forces that are sunnnarized 
undei' tlie term weather. The variation in the (juantity 
of the I'aint'all is one of the weatlier changes known to 
(ia\'e a marked elVect upon the yield of the crops, and 
if this fact is taken into con>idei'alion with t!ie preceding 
reasoning:, we ha\e a workinji; tiieoi-y as to the cause of 
l-",conomic Cyclo: The chaimcs in tlie weaUier repre- 
seiited hy the chanjies in the ([aantity of rainfall cause 
the chanjres in the yield per acre of the crops, and the 
variations in the yield of the crops cau-e the economic 
chanjies known as |-!conomic Cycles. With this work- 
\\\]l theory in mind, we examined a])i)ro]ii''.ate data with 
refei'eiice to three thiiiir-: iji 'l"he pei'iodicity of rain- 
fall; '-'i the eftect of rainfall on the cro])^: i)^) the rela- 
tion of tic >ield of the crojis to IVoiiomic ( 'ycles. 

l'"ir-t, then, as to the peiiodicity of rainfall. The 
pi'olilem as to whether the ([uantity of rainfall j)assps 
throuiih defimie cycles invohes two practical ([UestioiiS 
that af.ect the utility and tlu- validity of the results that 
may he att.-ii'ied. These (|uestion< are, first, as to what 
rainfall data shall he used in the investijiation of possible 
rainfall c\cli's; and, second, a- to the method that .shall 



Sitnintiirj/ (UkI ('(iiicha^Kui.s 



137 



1)(" ;i(l()|)t('(l to establish tlic ("xistciu'c of the cycles and 
to ascertain their characteristic lenfz;ths. amplitude's and 
phases. In our iiivestijiatioii, tlie choice of rainfall data 
was suf^K<'^t*'<l ''y <!"' scope of our s^^'ifi^'il prohloni. 
Supposint!; that we could find definite jieriods in the 
varying; amount of the rainfall, we should then desin> to 
know the relation of rainfall to the yield of th(> crops, 
and the relation of the yield of tlH> crops to Kcoiionue 
Cycles. It was necessary, then>fore, that the data 
of rainfall should refer to an area in which important 
crops are i)roduced, and it was desirable that the data of 
both rainfall and crops should refer to a hif^hly dynamic 
society. For these rea^^ons we collected the material 
for our investifiatiou from the central part of the United 
States. 

The method adoi)te(l in an investifjation of tlic 
periodicity of rainfall must satisfy three conditions: 
(1) It nuist exhaust th(> data in tlie search for possible 
cycles: that is to say. the data nuist be made to yield 
all the truth they contain nlatinu; to the jiarticular 
problem in hand. Freiiuently in th(> past, spurious 
periodicities have been presented as real periodicities, 
cliielly because the investigator start(Ml with a bias in 
favor of a particular j)eriod and tlid not i)ursue his 
researches sufficiently far to determiiu> whether his 
result was not one anions many s|)urious, chance 
periodicities coiitaiatMl in his mat(>ri;i I. In the search for 
real jH'riodicities the data must be exhaustively ana- 
lyzed. (2) 'I'iie method must render possible the (Hs- 
crimination between a true periodicity, haviufj; its 



138 



Economic Cj/clc:^: Their Ijiir and Cause 



origin in ;i imtunil cause and porsisting wi^li a chaiifio in 
till' samples of statistics, and a spurious p(>rio(licity 
wliicli is i)uroly formal, having its origin in accidental 
cliaracteristics of the statistical sample and disappear- 
ing, or radically altering its character, when different 
samples of statistics are made tlie basis of the comi)uta- 
tion. i'.i) 'Vhc m(>thod must not only make possible 
the isolation of real i)eriodicities, hut it must likewise 
enable one to determine their essential characteristics, 
their length, i)hases aiui amplitudes. 'Hie method we 
adopted in our researches, which i 'ias(>d upon the 
harmonic analysis, satisfies these three conditions. 

The result of our investigation as to th.e periodicity of 
rainfall in th(> (ipp(>r Mississippi \'all(\v was the dis- 
covery that the aimual rainfiill jiasses through two 
cycles of a])proximately thirty-three years and eight 
years in length. The amplitude and jthases of thes(» 
two cycles were ascertained, and the e(iuations to tlie 
separate cycle-; were cal('ulat(>d. Tlu^ two cycles wove 
then superposeil, tluis giving th(> geiKM'al cyclical mo\e- 
mcnt of rainfall; the (Mjuation of tliis compound cycle 
w:is computed and tlu^ graph wa- drawn, it was found 
that the curve of the I'hythmical moxiMueiii of rainfall 
computcnl from tlie (Miuation to the sui)erposed cycles 
lilted exc(>llently uell the actual ol)servations of rainfall. 
These results constitute the solution of thc^ first i)art of 
our general problem: Rainfall in the jirincipal crop area 
of the I'liitcd States passes thi-ough cycles of thirty- 
three y(>ars and of eight years. 

The caution that should be ol)serv('d in the use of our 



Sui'iiiKiri/ (iikI ( 'iixi'liisiunt- 



VM) 



('onclu-iniis is susificslcd liy the mctlKKl that was cm- 
l)l()y('(l and the siilijcct that was investigated. 'I'he 
ituHiiry is a >talistical stndy of an aspect of nietcdniln^y, 
and, tlierefnre, the eaiitinn to l)e exercised in tlie use 
ol' the conchisidns is the caution tliat should he ai)i)Hed 
to statistical worl< in jieneral and to nieteorolony in 
l)articular. As far as the statistical work is concerned, 
it Miould he ohseiNcd that the data were drawn I'roni ii 
limited area of th(> liiited States and co\-ei'ed, at most, 
seventy-two years. Conseiiueiitly, while there seem to 
he very jiood reasons in favor of the helief that, for th(> 
purpose for which they were used, the data were repre- 
sentative of the whole country, it is highly desirable 
that similar studies should be made for other places and 
other times. Furthermore, the present invest ifj;at ion 
was limited to a study of tlie periodicity of rainfall, but 
a more adeiiuate res(>arch would embrace the periodicity 
of temperature and of other we.Uher elements. toji(>t'«.er 
with an invest ifiat!oi> of the interrelation of the (>l"meuts. 
Hefore p.assin^ on to consider the caution to be observed 
in the use of statistical studies of meteorology, a word 
should i)e said in justiiication of the limitation of the 
incjuiry to the periodicity of annual rainfall. The ob- 
ject of taking aruuial rainfall was to ascertain the mean 
periodicit\- of th(> rainfall of the critical seasons of tli(> 
several crojo. It would haxc been more satisfactory to 
investigate the periodicity oi the r.iinfall of the <-ritical 
season in case of each cro]), but, becau-e of the extreme 
latxiriousness of the calculations, a device had to be 
adopted to limit the an.ount of computation. 



140 i!ciiii(niiiv Ci/clcs: Thrir Lair uml ('ausi' 

III rcKiird to the use of siatistical jiciiciMlizat ions in 
n;<'t('oi-olot;y, we li;i\c llir cautious opinion of I.onI 
Kchin: " I cannot say wlictlirr anytliiny; with icfcrcncc 
to 'I'crrcstrial Mctcorolojiy is done once tor all. 1 
think i)rolialily the woik will never lie done." IIhtc 
is always need of checking up statistical conclusions in 
the li^ht of new data, and this necessity applies to the 
Ijoneralization that in the Mississi])))! N'alley tlio annual 
rainfall passes throujih a doulile cycle of thirty-three 
yours and ei^ht year>. '{"his ci)nclusion is luidouhtedly 
warranted hy the data that lie at the liasis of the in- 
vest ijiat ion, hut it would he a Kiave fault, indeed, to 
hold that the cycles do not ;il,er with the (low of tiin(>. 
Whether the>' ch.anjic oi' retain their characteristics can 
he determined only liy accunuilatini^ more data th.an 
are at present a\ ailaiile. 



We come now to the s(>cond jiart of our fieneral 
prohlein, namely, to the consid(Mation of th(> relation 
hotween I'ainfail and the yield of the crops, and afiain 
the (luestions of data and method must ])o settled. 
In choosing the data, the i)rime consideration was to 
make sure that the croi).- selectc-d should he repres(>nta- 
ti\'e of the conditions of crop-pioducin^ in the .Middle 
West, 'i'he live pirincipal crops in the Middle West ar(> 
rorn, h;iv, wh(>at, oats, and potatoe--, and of these live 
all except wheat wer<> t.nkiMi to serve as re])resentative 
crops. Wheat was omitli-d because of tecluiic.al dif- 
ficulties: I'irst.it is impos.-^ihle, except for recent years, 
to separate in the pul>lishe(i statistics the yield i)er acre 



Siuni/Kirij mill ('imiiusions 



141 



of spriiifi wlicat from the yield of wiiitrr whrat; aiul. 
s(-coiully. since tlic .rrowth s,.;,>ons niul criti.'al periods 
of these Iwo varieties of wheat are rUffcreiit. it seemed 
unwise to attempt to coiiiieet the rainfall of any season 
with the yield l>er acre of wheat in which the lijiures for 
the yield ref<M-red to sprin-: and winter wheat tak(>n 
together. For these reax.ns the rei.resentative crops 
were limited to corn, hay, oats, and potatoes; and the 
yield per acre of these several crops throughout a long 
period of time, togetlier witli the rainfall of their 
respective criti.'al seasons, form the numerical data of 
the inv(^stigation. 

The method of determining the critical reasons was to 
find, by the use of the stati>tical theory of correlation, 
the month or miuUlis, in th(> lifetime of the several 
crops, the rainfall of which gave the highest correlation 
with the ultimate yield. This preliminary iiuiuiry 
atTordcnl a i)artial an>wer to our general (luestion as to 
tho lelati.m l)etwe(>n rainfall and the ciops. We found 
that in case of each of the crops the yield per acre is 
directly conn(>cted with the rainfall of some critical 
p(-riod, and in all of the crops excei)t oats the connection 
is very close. It siM-med probable, therefore, that since 
the rainfall passes through definite cycles, and since 
the yield per acre of the crops is intimately related with 
the rainfall of their respective ( i ,!ical seasons, the yield 
per acre of the crops should likewise pass through the 
double cycle described by th.e rainfall of the critical 

seasons. 

The investigation of the relation of the cycles of the 



1J2 



ICroiiitiiiir ('i/clrt<: Their Law uml Ciiusr 



fT()i)s to tlic cycles of the rainfall of the critical seasons 
was carried out in two ways, lirst for the croi)s taken 
siiifily, and then for tlie crops taken all together. In the 
in(iuiry rei;itin}i to the separate crops, the equations to 
the (loul)le cycle in the yield per acre and to the double 
cycle in the rainfall ot the corroponding critical seasons 
were computed, and the ^I'aphs were ihawn. Wlien the 
graphs of the cycles of the crops were superposed upon 
the jjraphs of the cycles of rainfall of the res|)ective 
critical seasons, the two curves were found to present a 
very reinarkalile congruence. In the in(|uiry relating 
to the crops taken all together, an index luunher of the 
yield per acre of the crops and an index number of the 
mean effective rainfall of the critical seasons were con- 
structed. The e(iuations to the double cycle in both 
indices weic computed, their graphs were drawn and 
then superpo.-ed. It was found that th(> cliaracteristic 
features of the rainfall curve were reproduced in the 
curve of the index nunilier of the yield per acre of the 
crojis. 

These results, referring both to the crops taken singly 
arul to the croiis taken all together, are the answers to 
the second part of our general (}uestion: The yield per 
acre of the representative crops is closely connected 
statistically with the rainfall of the respective critical 
seasons, and the relation is so close that th(> cycles of 
the yield per acre of the crops re|)roduce in char- 
acteristic ways the cycles of the rainfall itf the critica' 
seasons, '['he fundamental, persistent cause of the 
cycles of croj)s is, tlierefore, the rhythmical movement 



SiniUNdri/ and Ctinrlusnins 



143 



in the conditions of the wcuthcr rcprosontcd hy tin- 
cycles in tlic amount of rainfall. 

In the cautious use of the preceding; generalizations, 
one will hear in mind that oidy four croi)s have l)iM>n 
invest if:at(Mi, and that, in ascertaining: the critical 
seasons, the monlldy rainfall has i)een used. TIk! 
critical seaons could undoul)t(>dly lie determined more 
accurately if the tiKures for the weekly rainfall were 
employed. Furthermore, the in<iuiry has heen limited 
to the relation of the yield of the cro[)s to rainfall, 
whereas a more adecjuate study would incUule at least 
the efl'ectsof temi)erature. 



Thus far the investipation has established the law 
and cause of the cycles of th(> crops; The cause of the 
cycles in the jdiysical productivity of the crops is the 
cyclical variation of the weather represented by the 
cycles of rainfall, and the law of the cycles of rainfall is 
the law of the cycles of the crops. In order to hrinp; 
these physical results into relation with the rhythmical 
movements of pric(>s aTid vahies. we had first to show 
how the i)rices of the several crops vary with their 
respective sujiplies. In technical terms, we had to 
discover the laws of d(-mand for the individual crops. 

The (Hiuations to the law of demand for corn, hay, 
oats, and potatoes wer(> computed, and the {graphs were 
drawn. The dv^rcv of i)recision with which these 
demand curves miiiht he umhI as formuUe for predicting 
prices was ascertain(>d, and the coefhcients of the 
elasticity of demand for tlie representative commodities 



lit I'.x'iiiidtiiir Ciidi .<: Thrir ijiif tmil diiisr 

\\('l-(' calciilali-il. 'I'lir (■(|il;il inti-- In the law nf dctiialiil 
I'nr ail t'lMir crdp- cniil'iir;!!!'!! In a ^iiinlr type, iiidirat iiiK 
tlial as the Mipply rl' tlic i-niiiinndi! \' iiincaM's, the pi cc 
falN. I'nr rca^nii- that wen' cxplaiiicil in the disciis-ioii, 
we iiaiiicd this type nf dcinaiid ciiivc the Mcji,alivc lyj)i'. 



It will he recalled that itie ;lii-ee di\i>inllS of iilir 
general pi'nhlerii were ili the peiindieity nf rainfall; 
(2i tli(> effect (if rainfall iipnii the ernps; and Ci) the 
relation of the yield of the ci'ops to Ilconomic Cycles. 
The elalioration of a method foi' calcidatin;: the deniaiid 
ciii'ves plai'cd u> in po>itioii to examine the tliiid and 
linal paft of the prolilein. 'I'tie law of demand foi- the 
crops connects the price of the se\-eral crops with their 
re<pe('li\(' sujiplies. Imi the .-npply i-' dei)endeni tipon 
hotli tlie yield i)er acre and the extent of the acreaf^c. 
in order to hrini: our iindinjis with rofjard to the jH'riod- 
icity in the yield per acre into relation with ])rices and 
values, it is clear that we must kin.-w the relation 
l)etw<'i'ii the \aiiation in the price of 'he commodity 
and the yield jier acre of the commodity 'i'his ((ues- 
tion we examini'd at length, and found the tie lictween 
price and yield per acre to he as close as the tie lietweeii 
price and su!)])ly. To diffcM'cntiate hetween demand 
cur\('s and cm es showiiiii the relation hetween yield 
per acre and prii'c, we called the latter curves, yield- 
price cur\'es. We deduced thi' e([Uation> to the >'ield- 
price curves for the four representative coinmoditios 
and measured the dejiree of i)recisioii with which tluMr 
eouations miuht he used as formida' foi- predictine 



Siiintniini innl ( 'iiiichtsiitns 



145 



l)rii'i'<. In all "f tlu-i" n latinii-. the yirld-piicf curvos 
wrfc Iniind til he a> aciMiratc ami a-- -ali-fai-lmy as 
the (li'iiiaml I'UiA r- tlirm-fi\ I-. 

Witli the i)n--(--i(iii n|' the vidd-liriff curM-, <lici\\iiit; 
tlic rclaliini lirtwcrii tlir prices of the vvi^])< and tlirir 
vaiyiiiii yield in-r aere, it iniuhl >eeiii tliat the |iiiii.]eiii 
ol'amii'ulliiral cNcles at lea^t was (■ninpl'''''l> eliienlated. 
As we know liow liie jieiiodicity in the yield "i the emps 
follows tipnii the peiiMdiciiv in the rainfall, and Imw llie 
prices vary with the yield, one niijiht conclude that 
tlie cour-e of prices could he preilicted for a lon^ lime. 
The inference would lie entiicly true hut for the tact 
th.at the demand curves and the yield-price cur\i's move 
alternately up and down with the flow <'f time. This 
{■om|>lication made it nece><ai'y to investiirate the 
rh'-thiuical movement of the yield-l)rice cur\-es, imd 
\\c found tliat the demand cuiao, or yield-iirice curves, 
ri.se or f.all with the level of ^ent ral prices and with the 
level of the index ot the yield per acre of the cro!)s. 
The precedinu: fact- seemed to in\-ol\-e a contradiction 
with an " pnOri docti'ine of theoretical economics. 
Acconlinfi to the economic do<im;i of the uniforinity of 
the demand function, all ilemand curves are of the 
iiofiative type; As the amount of the connnodity in- 
creases, the price falls. Hut ,, this l.e true, how is it 
possible for a fall of fieneral prices to accoin|iany a fall 
in the index of the yield per acre of the crop.-? If the 
yield \n-v acre of tiu' cro|)s deci.ases. then, according to 
the yield-i)ric(,' curves and the d(-iaaiul curves, the i)rico 
of the croiis will rise. Moreover, as the ]irofits of trade 



1 It) /■'ciihdinir ('i/iiis: Till II l.iiii mill (iiusr 



.•iimI cciiniiiciic arc laindy (lr|Mii(|(nt uimn ihc \ulimi(' 
III ilic (Mill)-. It -I'l'iii- likely iliiit ihc ilfiiiMiid I'lf p'licnil 
(■iiimiinilit if- wniiM (|ccic;i-c w 1 1 1 1 a ( Icliciciicy ill the 
liar\ i--t -. aiiil, arcurdiiiL; In the (loiiuia nl llii' iiiiilni'inil \' 

hI tlir (Iniiailij I'lllH IMII. till' pricr- nf general ri'llllll(i(ii- 

tics >|ii]iii(i ri-r. Thr ulliinalc iT-iilt iil' liad liar\rsls, 
llicM'riirc, wiMilil lie a li-f in nciicral piiri-. The i'wiri, 
liii\\r\ cr, lirar mil the contrary view, ( Iciicral |iric<'S 
lall with ;i (jccr.aM' in ihc yield per acre nf ihe cruiis. 
A cdn-ider;! inn nf llii< ditiiculty led In ilie di-cnvcry 
ilia I I here i- a pii-ili\ e I y pe nf demand cur\ e as well as ji 
rieua'i\e Kjie. I nr a i-ei>re>eiitat i\e jirndiicer's (iiKid, 
fnr example iiisi-irini. l! e law n\' deniand i- -iicli that as 
the aiiiniiiil i>i cniiiiiindity increa>i'> the piice nf the 
1 niiiinndiiv rises, and as tie ainnuiil nf ihi' cniimmdil y 
decreases thi' urice nf tlie c(iniiiindily fall-. The e.xist- 
ei'.ce (if linlh iin,-iii\-e and ncf^alixc tyiie> nf demand in a 
liiKlih dynamic -nciely siinjiesled a wnrkmt; theory 
which ,-eemed In accnimt fnr liie inteirelatinn of all 
the known rele\anl facts, and which m.iy he stated in 
coiiipacl fnrni. The ih> thinically \ar.\inti >iel(l j'er 
acre ol the cmps ,- the caiiM' of licononiic ('ycles: 
Whoii the _, ielil increa-es, the Noliinie of trade, the 
activity of industry and the amount of employment 
increase; tiie demand for producers' tii'nds increases and 
the price- nf prnducei-' tinnd> rise: the demand ciirNcs 
fnr ;ifiricultiiral cnminnditie.- rise; with the ultimate 
rt'sull nt a ri-e nt general places. Thecnnlrary chan^jes 
would fnllnw ujinii a fall in the yield per acie of the 
crnps. 



SiiiiiiiKini ilii'l < 'iini hisitms 



\a; 



R<.y(.ii<l whai ur \vm\ ii1icm(1\ .-l;il.li~hr.l, \\u< tlicuiy 
(if th" intcrrcliitidii of re. iK-mic chiiiin''^ nMiuiiv.! tnr 
itsc(,ill|>lr1r(lcliinli-t|-aliu|i llic JM-o-.f (if the .■\l-triirr of 
t\V(.fuii.l;.inciit:il ivlal ini,^. luuit, that the cyli^ iii tlir 
yield iMi- acfc "f tlir cmp- arc ivpicdiUTd 

(1; ill ihcactiMty nf uninal iiidii-try; 
(2) ill tin- inn\ciiu'iit n\ ticiH'i-al inicc^. 
Til order to t(-t wlictlicr thiM' ivlatioii< actually i'\i>t, 
nil index inuiilKr of the yield per aeiv of the crops was 
constructed for the nine cro!>-^. '■ ", wheat . oat<. Laricy, 
ry.., Iiiickwhcat, iiay, cotton, an.! potalo.'s. 'I'o make 
sure of keei-inn clo>e to th.' rcMilts alrca<iy c-tahli-hed 
for the rei)re-entativ(- coniinodit ic- corn, liay. oat-, and 
potato.'s, the correlatioi; of tlie index of the nine crops 
with the index of tlie tour repri'seiitativc crops was 
coiujiuted and found to lie .' .'.tt'tt. 

.\> the production of pit:-iron is t;. nerally renarded as 
a KO"<l ••liaronieter" <if llie ac;i\ily <'f '.iKluslry. we 
soutilit an answer to the atiove first ((U.-lion liy in- 
vest iuatin<i whether the cycles in the yield lier acre o^ 
the nine crops were rei)roduced in the cyr'lcs in the 
pnuluctiop of pi^-iron. The in-iuiry involved the 
problems of the sei)a ration .if the cy.lical an.l the >.rular 
ninvenu'iits in the ].r.idu.'ti.in .if iiisr-ir.iM, and the 
ascertaiiunent .if the amount .-f the hm in the .-ycles 
of pi^-ir.in liehind the .'ycles i,, the yiel.l i-er a.ar of the 
crops. We f.iund that it take> l-etweeii .me aiid tw.) 
yeiir> iV,r the stimulation of incrcasint: harvests to w..rk 
out its maxinmm effct in promotinji the a.'tivity of 
industrvas tl;at activity i> rei)re>ented in the. ••haroiu- 



14S Ecomniiir Cjirhs: Thi ir Law mid ('misc 

ctcr" (if imlustry, the priidiictidii of pifr-ii'dn; and 
that, \v!i('u ail allowance is made for a la^i oi" two years 
in the acljustniciit of the pi^i-iroii industry, the cyclos 
of the yield Mer acre of the crops are u<'iierally rejiro- 
diiood in the cycles of the production i,f pifr-iidii, fho 
relation l>eiii<>- so dose that the coefiicient of coirelation 
ii r = .718. 



To fnid th(> relation of tie <'ycles in the yield j)er acre 
of the croj)s to the cycles in the movement of fxeneral 
prices, we made use of an index numl)er of general 
prices extendiiifi fron. Is7() to I!»l(). and of our index 
number of the yield per acre of nine crops co\ering the 
same interval of time. 'I'lie problem of sej)aniting ; 
eyrlieal mo^v■nlents in these two s(>ries from thoir 
.secular movements was solved, and tlu^ lag of the cycles 
of general [.rices behind the cycles in the yield of crops 
was f(!(ni(l to \)v alxiut four years. The coellicient of 
correlation ix-tween the cycles in th(> yield of th(> croi)s 
and the cycles in ttie g<'neral i)rices lagging four years 
behind the crop ■ vcles reached the very liigli value 
r = .800. When the lagging cycles of g( neral prices were 
plotted and their graph ^uperj)o^ed ui)on th.e graph of 
the cycles in the yield per acre of tii<' crops, the two 
curves were found to present a degree of eongruenee so 
close as to justify our working theory that the fun- 
damental, persistent cause of tne cycles of prices is the 
rhvthiiiical movement in the yield {)er acre of the crops. 
The cycles in the yield jier acre of the croi)s are followed 
at an interval of about two year> by the cycles in the 



f 



Sioniiiiirji (till! Cnncliisiottf^ 149 

activity of iiuiustry and ..f the v..lui. f trade, and at 

an interval of alx.ut four years in th(> cyeles of prices. 
Tliese conclusions l.nnml.t to a el<»e the last part of 
our general problem of the eause and law of Keouoniin 

Cycles. 

The links in the se(iueuee of causition were ooni- 
l)letely established: The fundamental, i)ersi<tent cause 
of the eyeles in the yield )f the (•ro])s is the cyeiicul 
movement in the weath(>r conditions represented by the 
rhytinnieally chansi'iJi amount of rainfall; the cyclieal 
movement in the yield of the croi>s is the fundamental, 
p(>rsistent cause of l^conomie Cycles. 



In the Intn; etion to this llssay it was ob>erve(l that 
economic dynamics stands in ne(>(l of a law that shall 
be to a chanjiinp society what the law of diminishing 
returns is to a society in a relatively static state. We 
may now formulate the law: The weather comlitions 
represented by the rainfall in the central part of the 
United States, and probabl., in other continental areas, 
liass through cycles of ai)proximately thirty-three years 
and eight years in duration, causing like cycles in the 
yield per acre of the crops; these cycles of crops con- 
stitute tlu- natural, material current which drags upon 
its surface the lagging, rhythmically changing values 
and prices w . which the econ.omist is more immedi- 
ately concer,,>'d. 



i mllbn books l.ythfsnnc author. 



LAWS OF WAGES 

AN ESSAY IN STATISTICAL ECONOMICS 

15V llLNItV l.ri.\MI.l. MooHl. 



Profi'SHiil- nl' I'.ililical i;r..h.iii<> 111 
('illullll)l:l llUViTSlty 



Ltollt. >;.W, ml. 



Extract frnin ili- Intni.lurtinn; - In thf fi.ll.winn chapters 
I have cmli avmvil to u>r tlic ncwrr >tutiMiral inrtho.ls and 
(hi. m.irr r.Mvnt crouoinir theory to extrart, from data re- 
latin- to xva>ie>, either new truth or else truth m sueh new 
form'as will admit oi it.- 1.. nm l.rounht into fruitful relations 
with the generalizations of economic scu'nce. 



CONTEXTS 



lutruJuction 



PAGE 
1 



CllAI'TIK I 

Sldli.-ilinil l.nir> 



A Srattcr Diaeram 
Definition of Terms 
(■lianictcii>tics of Stiilistinil l.:i\\- 



II 
l.'i 
21 



('iiAi'Tiai 11 

]r./;/..s, M'lus of Suhsi.Unn . ■/'"/ tin -'nfuhtr^l nf I.ifr 

Dosrription nf Oata 

Wascs ami tlie Means ef Siilisistence 

Wates ami llie Staliilanl I'f Life 

Wages of SkiUed and wf I'nskilk'd I.aherers 



20 
■J'.) 

no 



Chapteu tit 



4r> 



Desrription nf Data ■; , ■ .. \- i , ,■ ,i,.. l>r, > i,t .le, 

Huctuations in the Rate of W agw and m the \ alue .-t tlie I n n t t'. 



LAWS OF WAGES hy Henry Ludwdl yioon— Continued 

COSTESTS—Cuidinued p.u.e 

riurtuatinns in ilu' LulxiriT's Relative Share of the Product and in 

thi' liatio (,]■ Ciipiial t.i I, il)(]r "j.j 

'I lie Clt'iieral Trend oi Wane:- tjl 



(lUI'llli l\ 

n,n,,. „,„/ Mullll, 

\ii llypnthesi^ a- til llic I )i~iiiliiiiiiiri .'t \liihl> 
(iiouiids Icir the lly|iolhe.-i~ 

'The I'Apressioii of the < iau~>i:iii l.aw ilia luiiiilhal uill iiiilati 
the ■restiiii; of tlie 1 Jill.iviiiiil IIm' iry of \\ a^es 

I lie Staiiilard I'opiilalion 

The Application ..f the I leiii\ ,,| the Sliiid:ir.| rnpiilalion. . 
I{i'iiiurk upon the I'reri dini; Deii.inistratiori 



7t 

7ii 



S.l 



CliMTKIl \ 

II'./(/(.^ (inil Slriken 
Outcome of Strikes a,-> affected l.y ihe Sirnitth nf Ti-idi.— riiidiis 1(1.', 



OulcoMie of Strikes a,- hliiited liy 1 aMii.iiiiir Law 
■•uiuiiiarv 



121 
1:54 



CllAI'TKll \1 

U'df/es iiml Ihi Conn ntnitiDii nf Intin.^irfi 

NVapes as affei'ted hy the Coiicentratinii of Indii-try 
Amount of Kliiployiiieiit 
("oiitinuity nf lan]iln\ iiieiit 
Length of Working Day 



ItO 

!.■.{ 
l.-,li 
llil 



ClIArTKK \ II 

Statistical Fi'iiiioiiiirs and Industrial Leiiislatinn 
Fraetiral Aspi els i)f the I'esults of I'reeedim; ('ha|>ter> 
Statistical la niininies anil Svnlhetie lieoiKniiies 



in 

I'.tCi 



COMMI'XTS OI" SPl'CI AI.ISTS 

"Professor MiM.re l)iint;s tn hi~ task a wide ac(]uaintance with the 
most dilhiaill part~ nl' llie liieratore of eednnmies and statistics, a full 
al)i)reciation of its larize prolilenis. a judicial spirit and a dif^niiied style." 
I'. W, TArssn,, in the (J'lnrh rh/ Jdunud af A'co/ioi/iir.s. 



"Statistics of the ordinary official kind have often served to support 
the arguments nf political I'conomists. Hut this is the tirsi (ime, we 
believe, that ihi hit;lier statistics, which are founded on the Calculus of 



LAWS OF WAGES tiy Honry I.ixlwcll yimre— Continued 

Probabilitios, have born iis<-a on a lur^f' siali- as a buttress of economic 
theory" 1' ■ Y. Edcjeworth, in the Eatnomic Junrnnl. 



•■Professor Monrr has l)rokeii new (iroiiinl in a most interesting fielil, 
antl wliiie we in;iy dilT^T fn.iii huu in iIp' wi lijlil to l)e attadied In llcis 
lir that re-ult nr tb.' i.ii.-riin iMtmn I., be phieetl i>\\ some observ.-d e«>- 
rllieient, we may oiler rcnlial eoiinniiulations on the work as a hole. 
CJ. I!. Vl-LK, ill the Jountill e/ tin lii'U'tl -^V./Zi '-n,/ S,H-tilij. 

"Die I'ruclitbarkeit iI.t ver^.iidel.ri M.'tho.L' seheint mir (hireh 
(hese rntersuchimcen zweifello> ^rwiesen. .-benso uie(he Fr iehbarkeit 
lies Ziels, (he Theorie naliz chehl an 'iii' Zahleliauschueke der wirlschaft- 
Uchen Tatsaehen heran/,ubrin>:en. In.l .ku< ist eine Tat, /M der der Aulor 
TUir zu benluekuun>rhen ist, . . . liat .las Hueh aurl, o.f d, r Hand 
lieuend.' I'ehler in der Zukuii!! win! man mcIi mIiht als der er>ten 
klareii. eiiifa.'hen und ziellx'wnssten Darlemmn und KNiMiiphfi/ienim! der 
Anwenibmu der iiohcTen Statistik' auf ,,konomiselie Prol)ieme dankliar 
erinnern." .Io-i:i'ii Schumi-eter, m tlic Arclur far SoztulivtiMiischafl 
null Sozitilp'itilil-. 

■■Non seulement il nous enseigne Teinploi d'une m^thode (|ui dans de 
certaines hmites ]). : etre tri'S f^'.eonde. Mais eneore son habilett'- 
personnelle dans le inanienient de eette ini^'thode est trjs reelle. 11 salt 
seriiter les statisticnies d'une faeoi. fort i)6netrante et exposer les rC- 
miltats de ses reelierehes avee beaueoup d'eletrance. I e leeteur fraiic.'ais 
en partieulier, appreeiera I'inneniosite avee laquell.^ il tire des stalistiipies 
franvaises des inductions souvent nouvelles et ju.-tes." Alhkiit Aita- 
LKiN, in till' llmw d'kistoirf '/es (todriiws tronomiqui.-i. 

••Aleuni del risultati ottenuti .laH'autore, sono nuovi e suw^tivi 
e da essi molte eonelusioni si possono trarre (eui rautore aeeenna lu'l 
eapitolo finale ilella sua op.'ral sia rispetto alle teorie del salario .•he 
risiK-tto alia politiea soeiale. U libm e insomnia, ripetiamo. un con- 
tributo moho iinportante all'investiuazione seientifiea <lei feiiomeni 
eeoiiomiei <■ vorremmo ehe esso stimolasse pareeehi altri studiosi a far.' 
Iier allre indii.strie o per altri paesi, reeerehe analoghe. Constantino 
BnEsciANi TuiiuoNi, in the CwnuiU 'l,ijli Kroiuimi^li. 



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